%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SCT024-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 17:42:39 EDT 2024

% Result   : Unsatisfiable 2.27s 2.49s
% Output   : Proof 2.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.21  % Problem    : SCT024-1 : TPTP v8.2.0. Released v4.1.0.
% 0.22/0.22  % Command    : do_cvc5 %s %d
% 0.22/0.43  % Computer : n023.cluster.edu
% 0.22/0.43  % Model    : x86_64 x86_64
% 0.22/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.43  % Memory   : 8042.1875MB
% 0.22/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.22/0.43  % CPULimit   : 300
% 0.22/0.43  % WCLimit    : 300
% 0.22/0.43  % DateTime   : Mon May 27 18:09:24 EDT 2024
% 0.22/0.43  % CPUTime    : 
% 0.47/0.73  %----Proving TF0_NAR, FOF, or CNF
% 0.57/0.73  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.27/2.49  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.Fpm6wbrBOy/cvc5---1.0.5_13943.smt2
% 2.27/2.49  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.Fpm6wbrBOy/cvc5---1.0.5_13943.smt2
% 2.27/2.52  (assume a0 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 2.27/2.52  (assume a1 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.c_Transitive__Closure_Ortrancl V_s T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 2.27/2.52  (assume a2 (forall ((V_A $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_u $$unsorted)) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBB (tptp.c_Set_Oinsert V_a T_b) V_B (tptp.tc_fun T_b tptp.tc_bool) (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a (tptp.tc_fun T_b tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_b) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)))) (not (tptp.hBOOL (tptp.c_in V_u V_A T_a))))))
% 2.27/2.52  (assume a3 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Osym (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_s) T_a) (not (tptp.c_Relation_Osym V_s T_a)) (not (tptp.c_Relation_Osym V_r T_a)))))
% 2.27/2.52  (assume a4 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_a T_b) (tptp.tc_prod T_a T_b)) V_r) T_a T_b) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Relation_ODomain V_r T_a T_b)))))
% 2.27/2.52  (assume a5 (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) V_A) V_x))))))
% 2.27/2.52  (assume a6 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A)) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A))))
% 2.27/2.52  (assume a7 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B)))))
% 2.27/2.52  (assume a8 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a9 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.tc_fun T_a tptp.tc_bool)) V_B))))
% 2.27/2.52  (assume a10 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))))
% 2.27/2.52  (assume a11 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A) T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a))))))
% 2.27/2.52  (assume a12 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))))
% 2.27/2.52  (assume a13 (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_A (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a14 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB (tptp.c_Set_Oinsert V_a T_a) V_B (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a15 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B)))))
% 2.27/2.52  (assume a16 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a17 (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Transitive__Closure_Ortrancl V_S T_a)) (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S) T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))
% 2.27/2.52  (assume a18 (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_c $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_c (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBB (tptp.c_Relation_OImage V_r T_b T_a) V_B (tptp.tc_fun T_b tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_c) T_c (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a19 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))
% 2.27/2.52  (assume a20 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a21 (forall ((V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Relation_ORange V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_ORange V_B T_b T_a)) (tptp.c_Relation_ORange (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_B) T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a22 (forall ((V_A $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a23 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a24 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))))))
% 2.27/2.52  (assume a25 (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_C (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b T_a) (tptp.c_Product__Type_OSigma V_B (tptp.c_COMBK V_C (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b T_a) (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_C T_a))))))
% 2.27/2.52  (assume a26 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_C (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b T_a) (tptp.c_Product__Type_OSigma V_B (tptp.c_COMBK V_C (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b T_a) (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_C T_a))))))
% 2.27/2.52  (assume a27 (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a28 (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a29 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a30 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_A))))
% 2.27/2.52  (assume a31 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f (tptp.tc_fun tptp.t_a T_b)) V_g) tptp.v_x) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) T_b) (tptp.hAPP V_g tptp.v_x))))))
% 2.27/2.52  (assume a32 (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Relation_ODomain V_A T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_ODomain V_B T_a T_b)) (tptp.c_Relation_ODomain (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) V_B) T_a T_b) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a33 (forall ((V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.tc_fun T_a tptp.tc_bool)) V_A)))))
% 2.27/2.52  (assume a34 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a35 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_z))))))
% 2.27/2.52  (assume a36 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z) T_a) V_x) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_x) T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z T_a) V_x))))))
% 2.27/2.52  (assume a37 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Relation_OId__on V_A T_a) (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))
% 2.27/2.52  (assume a38 (forall ((V_r $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 2.27/2.52  (assume a39 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A)))
% 2.27/2.52  (assume a40 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_x) V_x))))
% 2.27/2.52  (assume a41 (forall ((V_r_H $$unsorted) (V_s_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_r_H V_s_H T_a T_b T_c) (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) (not (tptp.c_lessequals V_s_H V_s (tptp.tc_fun (tptp.tc_prod T_b T_c) tptp.tc_bool))) (not (tptp.c_lessequals V_r_H V_r (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 2.27/2.52  (assume a42 (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_S $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_S) T_b T_a) V_A) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Relation_OImage V_S T_b T_a) V_A)))))
% 2.27/2.52  (assume a43 (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) V_B)))))
% 2.27/2.52  (assume a44 (forall ((V_P $$unsorted) (V_Rb $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_Rb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Osko__Recdef__Xtfl__wf__induct__1__1 V_P V_R T_a)))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 2.27/2.52  (assume a45 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) V_A)) (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A)))))
% 2.27/2.52  (assume a46 (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))))
% 2.27/2.52  (assume a47 (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)))
% 2.27/2.52  (assume a48 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B))))
% 2.27/2.52  (assume a49 (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b (tptp.tc_fun T_a tptp.tc_bool)))) (= V_C (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))
% 2.27/2.52  (assume a50 (forall ((V_xa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oinsert V_xa T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))))
% 2.27/2.52  (assume a51 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_b) V_C) V_B (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_B (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 2.27/2.52  (assume a52 (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_xa T_a) V_y) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x T_a) V_x))) (= V_xa V_y))))
% 2.27/2.52  (assume a53 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x T_a) V_x) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x_H T_a) V_y_H))) (= V_x_H V_y_H))))
% 2.27/2.52  (assume a54 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_B T_b T_a)) (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B) T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a55 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a56 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a57 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a) V_z) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z))))))
% 2.27/2.52  (assume a58 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_z))))))
% 2.27/2.52  (assume a59 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_z))))))
% 2.27/2.52  (assume a60 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a) V_z) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z))))))
% 2.27/2.52  (assume a61 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_A) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a62 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_B) (not (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a63 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_x) (not (tptp.c_lessequals V_x V_y T_a)))))
% 2.27/2.52  (assume a64 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_x)) (tptp.c_lessequals V_x V_y T_a))))
% 2.27/2.52  (assume a65 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_y) (not (tptp.c_lessequals V_y V_x T_a)))))
% 2.27/2.52  (assume a66 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_C (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a67 (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a68 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a69 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_C (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a70 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))))
% 2.27/2.52  (assume a71 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a))))
% 2.27/2.52  (assume a72 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a))))
% 2.27/2.52  (assume a73 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))))
% 2.27/2.52  (assume a74 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))))
% 2.27/2.52  (assume a75 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a))))
% 2.27/2.52  (assume a76 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a))))
% 2.27/2.52  (assume a77 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A))))
% 2.27/2.52  (assume a78 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 2.27/2.52  (assume a79 (forall ((T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a80 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a81 (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a82 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B) T_b T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_B T_b T_a)) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a83 (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) V_B)) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a84 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)))) (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a85 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C))) (not (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a86 (forall ((V_I $$unsorted) (T_a $$unsorted) (V_J $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_I (tptp.tc_fun T_a tptp.tc_bool)) V_J) V_C T_a T_b) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Product__Type_OSigma V_I V_C T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Product__Type_OSigma V_J V_C T_a T_b)))))
% 2.27/2.52  (assume a87 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_A)))
% 2.27/2.52  (assume a88 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a89 (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_C (tptp.tc_fun T_c tptp.tc_bool) T_a) T_a T_c) (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) (not (tptp.c_lessequals V_s (tptp.c_Product__Type_OSigma V_B (tptp.c_COMBK V_C (tptp.tc_fun T_c tptp.tc_bool) T_b) T_b T_c) (tptp.tc_fun (tptp.tc_prod T_b T_c) tptp.tc_bool))) (not (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_B (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 2.27/2.52  (assume a90 (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S) T_a) (not (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_R V_S T_a T_a T_a) V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Owf V_S T_a)) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 2.27/2.52  (assume a91 (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x))))))
% 2.27/2.52  (assume a92 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))))
% 2.27/2.52  (assume a93 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))))
% 2.27/2.52  (assume a94 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Orefl__on (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_s) T_a) (not (tptp.c_Relation_Orefl__on V_B V_s T_a)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 2.27/2.52  (assume a95 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) T_a) V_z) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z))))))
% 2.27/2.52  (assume a96 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_z))))))
% 2.27/2.52  (assume a97 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_z))))))
% 2.27/2.52  (assume a98 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) T_a) V_z) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z))))))
% 2.27/2.52  (assume a99 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a100 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a101 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x))))
% 2.27/2.52  (assume a102 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x) V_x))))
% 2.27/2.52  (assume a103 (forall ((T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_B)))
% 2.27/2.52  (assume a104 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_A)))
% 2.27/2.52  (assume a105 (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a106 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A) (tptp.c_COMBK (tptp.hAPP (tptp.c_Set_Oinsert V_b T_b) V_B) (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b) (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_a T_b) (tptp.tc_prod T_a T_b)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK (tptp.hAPP (tptp.c_Set_Oinsert V_b T_b) V_B) (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A) (tptp.c_COMBK V_B (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b))))))
% 2.27/2.52  (assume a107 (forall ((V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.tc_fun T_a tptp.tc_bool)) V_B)))))
% 2.27/2.52  (assume a108 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a109 (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))
% 2.27/2.52  (assume a110 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_C (tptp.tc_fun T_a tptp.tc_bool)) V_D) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_D V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a111 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_z)) T_a))))
% 2.27/2.52  (assume a112 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.tc_fun T_a tptp.tc_bool)) V_B))))
% 2.27/2.52  (assume a113 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y)) V_x))))
% 2.27/2.52  (assume a114 (forall ((V_P $$unsorted) (V_xb $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a115 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 2.27/2.52  (assume a116 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))))
% 2.27/2.52  (assume a117 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a118 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a119 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 2.27/2.52  (assume a120 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 2.27/2.52  (assume a121 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))))
% 2.27/2.52  (assume a122 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y)) V_x))))
% 2.27/2.52  (assume a123 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B)) V_A)))
% 2.27/2.52  (assume a124 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_x) (not (tptp.c_lessequals V_y V_x T_a)))))
% 2.27/2.52  (assume a125 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_y)) (tptp.c_lessequals V_x V_y T_a))))
% 2.27/2.52  (assume a126 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_y) (not (tptp.c_lessequals V_x V_y T_a)))))
% 2.27/2.52  (assume a127 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_B) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a128 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_A) (not (tptp.c_lessequals V_B V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a129 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_B)) (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a130 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a131 (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a132 (forall ((V_B $$unsorted) (T_a $$unsorted) (V_I $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_b (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I (tptp.c_COMBB (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a133 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_d T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (= V_a V_d) (= V_a V_c))))
% 2.27/2.52  (assume a134 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_d T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (= V_b V_c) (= V_a V_c))))
% 2.27/2.52  (assume a135 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_d T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (= V_a V_d) (= V_b V_d))))
% 2.27/2.52  (assume a136 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_d T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (= V_b V_c) (= V_b V_d))))
% 2.27/2.52  (assume a137 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 2.27/2.52  (assume a138 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.c_Transitive__Closure_Ortrancl V_s T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_lessequals V_r (tptp.c_Transitive__Closure_Ortrancl V_s T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 2.27/2.52  (assume a139 (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a140 (forall ((T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a141 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A)))))
% 2.27/2.52  (assume a142 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C))) (not (tptp.hBOOL (tptp.c_in V_a V_C T_a))))))
% 2.27/2.52  (assume a143 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))
% 2.27/2.52  (assume a144 (forall ((V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_Set_Oinsert V_a T_b) V_B) T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a)))))
% 2.27/2.52  (assume a145 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C (tptp.tc_fun T_a tptp.tc_bool)) V_D) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_D (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a146 (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_s) T_b T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Relation_Oconverse V_s T_b T_a)))))
% 2.27/2.52  (assume a147 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_x T_a))))
% 2.27/2.52  (assume a148 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_y T_a))))
% 2.27/2.52  (assume a149 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 2.27/2.52  (assume a150 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 2.27/2.52  (assume a151 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))))
% 2.27/2.52  (assume a152 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_y T_a))))
% 2.27/2.52  (assume a153 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) V_x T_a))))
% 2.27/2.52  (assume a154 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_A (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a155 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_B (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a156 (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_C (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a157 (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_C (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a158 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.c_COMBK V_C (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_C (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Product__Type_OSigma V_B (tptp.c_COMBK V_C (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b)))))
% 2.27/2.52  (assume a159 (forall ((V_C $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C (tptp.c_COMBB (tptp.c_Set_Oinsert V_a T_a) V_B (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_C V_B T_b (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a160 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a) V_x) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_x) T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z T_a) V_x))))))
% 2.27/2.52  (assume a161 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_z))))))
% 2.27/2.52  (assume a162 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a163 (forall ((V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C (tptp.tc_fun T_a tptp.tc_bool)) V_A)))))
% 2.27/2.52  (assume a164 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) V_x))))
% 2.27/2.52  (assume a165 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))))))
% 2.27/2.52  (assume a166 (forall ((V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_A T_c T_b) T_b T_a) (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_b T_a T_c) V_A T_c T_a))))
% 2.27/2.52  (assume a167 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.c_COMBK V_C (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_C (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Product__Type_OSigma V_B (tptp.c_COMBK V_C (tptp.tc_fun T_b tptp.tc_bool) T_a) T_a T_b)))))
% 2.27/2.52  (assume a168 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y)))))
% 2.27/2.52  (assume a169 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y)))))
% 2.27/2.52  (assume a170 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B))))
% 2.27/2.52  (assume a171 (forall ((V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Relation_ORange (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun (tptp.tc_prod T_b T_a) tptp.tc_bool)) V_B) T_b T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ORange V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_ORange V_B T_b T_a)))))
% 2.27/2.52  (assume a172 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))
% 2.27/2.52  (assume a173 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_x) V_x))))
% 2.27/2.52  (assume a174 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A) V_A)))
% 2.27/2.52  (assume a175 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_z T_a)))))
% 2.27/2.52  (assume a176 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) V_z T_a)))))
% 2.27/2.52  (assume a177 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) T_a) (not (tptp.c_lessequals V_x V_b T_a)))))
% 2.27/2.52  (assume a178 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_x)))))
% 2.27/2.52  (assume a179 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_x)))))
% 2.27/2.52  (assume a180 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a181 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A)) V_B) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a182 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_y) T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) V_z)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_z)) T_a))))
% 2.27/2.52  (assume a183 (forall ((V_S $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (= (tptp.c_Transitive__Closure_Ortrancl V_S T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a)) (not (tptp.c_lessequals V_S (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_lessequals V_R V_S (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 2.27/2.52  (assume a184 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_A (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a185 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A))))
% 2.27/2.52  (assume a186 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (= V_a V_b))))
% 2.27/2.52  (assume a187 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C (tptp.tc_fun T_a tptp.tc_bool)) V_A)))))
% 2.27/2.52  (assume a188 (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a189 (forall ((V_I $$unsorted) (T_a $$unsorted) (V_J $$unsorted) (V_C $$unsorted) (T_b $$unsorted)) (= (tptp.c_Product__Type_OSigma (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_I (tptp.tc_fun T_a tptp.tc_bool)) V_J) V_C T_a T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Product__Type_OSigma V_I V_C T_a T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Product__Type_OSigma V_J V_C T_a T_b)))))
% 2.27/2.52  (assume a190 (forall ((V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) V_A) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))))
% 2.27/2.52  (assume a191 (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))
% 2.27/2.52  (assume a192 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a193 (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))
% 2.27/2.52  (assume a194 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))
% 2.27/2.52  (assume a195 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B)) (tptp.hBOOL (tptp.c_in V_a V_A T_a)))))
% 2.27/2.52  (assume a196 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.hBOOL (tptp.c_in V_a V_C T_a)))))
% 2.27/2.52  (assume a197 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_B (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a198 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a199 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A T_a) V_B) (tptp.c_Orderings_Obot__class_Obot T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 2.27/2.52  (assume a200 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A T_a) V_B) (tptp.c_Orderings_Obot__class_Obot T_a))) (= V_B (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 2.27/2.52  (assume a201 (forall ((V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.tc_fun T_a tptp.tc_bool)) V_A) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A))))
% 2.27/2.52  (assume a202 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B))))
% 2.27/2.52  (assume a203 (forall ((V_S $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_T $$unsorted) (V_R $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_S (tptp.tc_fun (tptp.tc_prod T_a T_c) tptp.tc_bool)) V_T) V_R T_a T_c T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_S V_R T_a T_c T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Relation_Orel__comp V_T V_R T_a T_c T_b)))))
% 2.27/2.52  (assume a204 (forall ((V_R $$unsorted) (V_S $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_T $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_R (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_S (tptp.tc_fun (tptp.tc_prod T_c T_b) tptp.tc_bool)) V_T) T_a T_c T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_S T_a T_c T_b) (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) (tptp.c_Relation_Orel__comp V_R V_T T_a T_c T_b)))))
% 2.27/2.52  (assume a205 (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun tptp.t_a T_b)) V_B) tptp.v_x) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP V_A tptp.v_x) T_b) (tptp.hAPP V_B tptp.v_x))))))
% 2.27/2.52  (assume a206 (forall ((V_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals V_C V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a207 (forall ((V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_C V_A (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a208 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) T_a)))))
% 2.27/2.52  (assume a209 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) T_a)))))
% 2.27/2.52  (assume a210 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))))
% 2.27/2.52  (assume a211 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a T_a) V_b) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))))
% 2.27/2.52  (assume a212 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a)))))
% 2.27/2.52  (assume a213 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y T_a) V_z) T_a)))))
% 2.27/2.52  (assume a214 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a215 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A))))
% 2.27/2.52  (assume a216 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_x)))))
% 2.27/2.52  (assume a217 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y T_a) V_x)))))
% 2.27/2.52  (assume a218 (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool)) V_B) T_a T_b) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_ODomain V_A T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_ODomain V_B T_a T_b)))))
% 2.27/2.52  (assume a219 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.tc_fun T_a tptp.tc_bool)) V_A))))
% 2.27/2.52  (assume a220 (forall ((V_R2 $$unsorted) (T_a $$unsorted) (V_R1 $$unsorted)) (or (tptp.c_lessequals (tptp.c_Wellfounded_Oacc V_R2 T_a) (tptp.c_Wellfounded_Oacc V_R1 T_a) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_R1 V_R2 (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 2.27/2.52  (assume a221 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B))))
% 2.27/2.52  (assume a222 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y)))))
% 2.27/2.52  (assume a223 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) V_y)))))
% 2.27/2.52  (assume a224 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a225 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b)))))
% 2.27/2.52  (assume a226 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a227 (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Transitive__Closure_Ortrancl V_S T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S) T_a))))
% 2.27/2.52  (assume a228 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))
% 2.27/2.52  (assume a229 (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a230 (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x))))))
% 2.27/2.52  (assume a231 (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x))))))
% 2.27/2.52  (assume a232 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Relation_ORange (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_a V_b T_b T_a) (tptp.tc_prod T_b T_a)) V_r) T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Relation_ORange V_r T_b T_a)))))
% 2.27/2.52  (assume a233 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) V_A) (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))
% 2.27/2.52  (assume a234 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a235 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (or (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a236 (forall ((V_f $$unsorted) (V_g $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b)) (tptp.hAPP V_g (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b)))) (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b)))))
% 2.27/2.52  (assume a237 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_Wellfounded_Oacyclic (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) (tptp.tc_prod T_a T_a)) V_r) T_a)))))
% 2.27/2.52  (assume a238 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))))
% 2.27/2.52  (assume a239 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))))
% 2.27/2.52  (assume a240 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))))
% 2.27/2.52  (assume a241 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) V_A) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))
% 2.27/2.52  (assume a242 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))))
% 2.27/2.52  (assume a243 (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a244 (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))))
% 2.27/2.52  (assume a245 (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a246 (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a247 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))))
% 2.27/2.52  (assume a248 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))))
% 2.27/2.52  (assume a249 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) V_A) T_a))))))
% 2.27/2.52  (assume a250 (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))))
% 2.27/2.52  (assume a251 (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))))
% 2.27/2.52  (assume a252 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))))
% 2.27/2.52  (assume a253 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) T_a))))
% 2.27/2.52  (assume a254 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_B) T_a))))
% 2.27/2.52  (assume a255 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B) T_a))))
% 2.27/2.52  (assume a256 (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))))
% 2.27/2.52  (assume a257 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a))))))
% 2.27/2.52  (assume a258 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))))
% 2.27/2.52  (assume a259 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) T_a)) (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))))
% 2.27/2.52  (assume a260 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_A) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_B))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B))))
% 2.27/2.52  (assume a261 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_A) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))
% 2.27/2.52  (assume a262 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a))))
% 2.27/2.52  (assume a263 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop T_a) T_a) V_x) V_x))))
% 2.27/2.52  (assume a264 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) V_x))))
% 2.27/2.52  (assume a265 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A T_a) V_B) (tptp.c_Orderings_Otop__class_Otop T_a))) (= V_A (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 2.27/2.52  (assume a266 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A T_a) V_B) (tptp.c_Orderings_Otop__class_Otop T_a))) (= V_B (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 2.27/2.52  (assume a267 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Otop__class_Otop T_a) T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 2.27/2.52  (assume a268 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x T_a) (tptp.c_Orderings_Otop__class_Otop T_a)) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 2.27/2.52  (assume a269 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a270 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) V_A)))
% 2.27/2.52  (assume a271 (forall ((T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_B)))
% 2.27/2.52  (assume a272 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a273 (forall ((T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a274 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a275 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a276 (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a)))
% 2.27/2.52  (assume a277 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 V_a V_b V_r T_a) V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a278 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) T_a) (not (tptp.c_lessequals V_x V_a T_a)))))
% 2.27/2.52  (assume a279 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) V_x T_a)))))
% 2.27/2.52  (assume a280 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a T_a) V_b) V_x T_a)))))
% 2.27/2.52  (assume a281 (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a282 (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals V_B V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a283 (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_f (tptp.tc_fun tptp.t_a T_b)) V_g) tptp.v_x) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_f tptp.v_x) T_b) (tptp.hAPP V_g tptp.v_x))))))
% 2.27/2.52  (assume a284 (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))))
% 2.27/2.52  (assume a285 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))
% 2.27/2.52  (assume a286 (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a287 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))))
% 2.27/2.52  (assume a288 (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_C (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a289 (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a290 (forall ((V_p $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Wellfounded_Owf V_p T_a) (not (tptp.c_lessequals V_p V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a291 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))))
% 2.27/2.52  (assume a292 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))))
% 2.27/2.52  (assume a293 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym V_s T_a)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))))))
% 2.27/2.52  (assume a294 (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))))
% 2.27/2.52  (assume a295 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic V_r T_a) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.c_Wellfounded_Oacyclic V_s T_a)))))
% 2.27/2.52  (assume a296 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted)) (or (tptp.c_Relation_Osingle__valued V_r T_a T_b) (not (tptp.c_Relation_Osingle__valued V_s T_a T_b)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 2.27/2.52  (assume a297 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.tc_fun T_a tptp.tc_bool)) V_D) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_B V_D (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_C (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a298 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a299 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) V_C) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a300 (forall ((V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B) V_M T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_M T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_B V_M T_b (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a301 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_ODomain V_r T_a T_b) (tptp.c_Relation_ODomain V_s T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 2.27/2.52  (assume a302 (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a303 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_C $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.tc_fun T_a tptp.tc_bool)) V_C)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_C)))))
% 2.27/2.52  (assume a304 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))))
% 2.27/2.52  (assume a305 (forall ((V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_C (tptp.tc_fun T_a tptp.tc_bool)) V_A)) V_A) (not (tptp.c_lessequals V_B V_C (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a306 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x T_a) V_y) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x_H T_a) V_y_H))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))))
% 2.27/2.52  (assume a307 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x T_a) V_y) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_x_H T_a) V_y_H))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))))
% 2.27/2.52  (assume a308 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a309 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a310 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_C) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) V_D) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_lessequals V_C V_D (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a311 (forall ((T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a312 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B) T_b T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_B T_b T_a)))))
% 2.27/2.52  (assume a313 (forall ((V_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.hAPP (tptp.c_Set_Oinsert V_a T_b) V_A) V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_B V_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a314 (forall ((V_r_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A_H $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.c_Relation_OImage V_r_H T_a T_b) V_A_H) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_b) V_A) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A_H V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_r_H V_r (tptp.tc_fun (tptp.tc_prod T_a T_b) tptp.tc_bool))))))
% 2.27/2.52  (assume a315 (forall ((V_r $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals V_r (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_A (tptp.tc_fun T_a tptp.tc_bool) T_a) T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a316 (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))))
% 2.27/2.52  (assume a317 (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.hAPP (tptp.c_Set_Oinsert V_c T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))))
% 2.27/2.52  (assume a318 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Wellfounded_Oacyclic (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) (tptp.tc_prod T_a T_a)) V_r) T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))))
% 2.27/2.52  (assume a319 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Oacyclic (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) (tptp.tc_prod T_a T_a)) V_r) T_a)))))
% 2.27/2.52  (assume a320 (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBB (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a321 (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBB (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B (tptp.tc_fun T_a tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a322 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) V_xa) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.c_in V_x V_xa T_a)))))
% 2.27/2.52  (assume a323 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a))))))
% 2.27/2.52  (assume a324 (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_B T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))))
% 2.27/2.52  (assume a325 (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a))))
% 2.27/2.52  (assume a326 (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) T_b) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (tptp.c_Set_Oimage V_f V_A T_a T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))))
% 2.27/2.52  (assume a327 (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a328 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (tptp.c_lessequals V_x (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))))
% 2.27/2.52  (assume a329 (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.c_lessequals (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_M T_a T_b) (tptp.hAPP V_M V_i) T_b) (not (tptp.hBOOL (tptp.c_in V_i V_A T_a))))))
% 2.27/2.52  (assume a330 (forall ((V_Q $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 V_Q V_r T_a) V_Q T_a)) (not (tptp.hBOOL (tptp.c_in V_xa V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a331 (forall ((V_Q $$unsorted) (V_R $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 V_Q V_R T_a) V_Q T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 2.27/2.52  (assume a332 (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a333 (forall ((V_B $$unsorted) (V_A $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (V_I $$unsorted) (T_b $$unsorted)) (or (tptp.c_lessequals V_B (tptp.hAPP V_A V_i) (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.hBOOL (tptp.c_in V_i V_I T_b))) (not (tptp.c_lessequals V_B (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a334 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.c_lessequals (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) (tptp.hAPP V_B V_a) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))
% 2.27/2.52  (assume a335 (forall ((V_A $$unsorted) (V_k $$unsorted) (T_b $$unsorted) (V_I $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_A V_k) (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_a (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_I V_A T_a (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_k V_I T_a))))))
% 2.27/2.52  (assume a336 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a337 (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Product__Type_OSigma V_A (tptp.c_COMBK V_C (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b T_a) (tptp.c_Product__Type_OSigma V_B (tptp.c_COMBK V_C (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_C T_a))) (= V_A V_B))))
% 2.27/2.52  (assume a338 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) (tptp.tc_prod T_a T_a)) V_r) T_a)))))
% 2.27/2.52  (assume a339 (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__XImageE__1__1 V_A V_b V_r T_b T_a) V_A T_b)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a))))))
% 2.27/2.52  (assume a340 (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 V_A V_b V_r T_b T_a) V_A T_b)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a))))))
% 2.27/2.52  (assume a341 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) T_a) V_a))))
% 2.27/2.52  (assume a342 (forall ((V_x $$unsorted) (V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S) T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a343 (forall ((V_x $$unsorted) (V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S) T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Transitive__Closure_Ortrancl V_S T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a344 (forall ((T_b $$unsorted) (V_A $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBK V_M T_b T_a) T_a T_b) V_M) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a345 (forall ((V_p $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Otrancl V_s T_a) (tptp.tc_prod T_a T_a))) (not (tptp.c_lessequals V_r V_s (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a346 (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBB V_f V_g T_c T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_c) T_c T_a))))
% 2.27/2.52  (assume a347 (forall ((V_A $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBK V_c (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)) V_c) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))
% 2.27/2.52  (assume a348 (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_B) V_B)))
% 2.27/2.52  (assume a349 (forall ((V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b (tptp.tc_fun T_a tptp.tc_bool))) V_A)))
% 2.27/2.52  (assume a350 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Set_Oimage V_f V_A T_c T_b) V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBB V_B V_f T_b (tptp.tc_fun T_a tptp.tc_bool) T_c) T_c (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a351 (forall ((V_A $$unsorted) (V_B $$unsorted) (V_f $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBB V_B V_f T_c (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Set_Oimage V_f V_A T_b T_c) V_B T_c (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a352 (forall ((V_B $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP V_B (tptp.c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1 V_A V_B T_b T_a)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a353 (forall ((V_B $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.hAPP V_B (tptp.c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1 V_A V_B T_b T_a)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a354 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a355 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))))
% 2.27/2.52  (assume a356 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a) (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a357 (forall ((V_R $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 V_R V_x T_a) (tptp.c_Wellfounded_Oacc V_R T_a) T_a))) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_R T_a) T_a)))))
% 2.27/2.52  (assume a358 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a359 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))))
% 2.27/2.52  (assume a360 (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 V_r V_x T_a) (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a361 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a) (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a362 (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_Orel__comp V_S V_R T_a T_a T_a)) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S) T_a) (not (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S) T_a)))))
% 2.27/2.52  (assume a363 (forall ((V_R $$unsorted) (T_a $$unsorted) (V_S $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S) T_a) (not (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_Orel__comp V_S V_R T_a T_a T_a)) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_S) T_a)))))
% 2.27/2.52  (assume a364 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Relation_ODomain V_r T_a T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_ORange V_s T_a T_a)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.c_Wellfounded_Owf V_s T_a)) (not (tptp.c_Wellfounded_Owf V_r T_a)) (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) V_s) T_a))))
% 2.27/2.52  (assume a365 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Otrancl V_r T_a) V_r T_a T_a T_a)))))
% 2.27/2.52  (assume a366 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 2.27/2.52  (assume a367 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 2.27/2.52  (assume a368 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))))
% 2.27/2.52  (assume a369 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))))
% 2.27/2.52  (assume a370 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp V_r V_r T_a T_a T_a) V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Otrans V_r T_a)))))
% 2.27/2.52  (assume a371 (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_Oconverse V_r T_a T_a)) T_a)))
% 2.27/2.52  (assume a372 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (not (tptp.c_Relation_Otrans V_r T_a)))))
% 2.27/2.52  (assume a373 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_B) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_a tptp.tc_bool)) V_B))))
% 2.27/2.52  (assume a374 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a)))))
% 2.27/2.52  (assume a375 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)))))
% 2.27/2.52  (assume a376 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a)))))
% 2.27/2.52  (assume a377 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))))
% 2.27/2.52  (assume a378 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 V_a V_b V_r T_a) T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a379 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a380 (forall ((V_P $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xa)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a381 (forall ((V_P $$unsorted) (V_Ra $$unsorted) (V_y $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_Ra)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_List_Osko__Recdef__Xtfl__wf__induct__1__1 V_P V_R T_a) T_a T_a) V_R (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 2.27/2.52  (assume a382 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a383 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 V_r T_a) T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a384 (forall ((V_r $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 V_r V_x V_z T_a) V_z T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a385 (forall ((V_x $$unsorted) (V_R $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 V_R V_x V_y T_a) T_a T_a) V_R (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a386 (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 (tptp.v_sko__Transitive__Closure__Xtrancl__Xcases__1 V_a1 V_a2 V_r) tptp.t_a tptp.t_a) (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a) (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a) (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a) (tptp.tc_prod tptp.t_a tptp.t_a)))))))
% 2.27/2.52  (assume a387 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Oacyclic V_r T_a)))))
% 2.27/2.52  (assume a388 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 V_a V_b V_r T_a) V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a389 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 V_a V_b V_r T_a) T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a390 (forall ((V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 V_R V_x V_y T_a) V_y T_a T_a) V_R (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a391 (forall ((V_x $$unsorted) (V_r $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 V_r V_x V_z T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a392 (forall ((V_a1 $$unsorted) (V_a2 $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.v_sko__Transitive__Closure__Xtrancl__Xcases__1 V_a1 V_a2 V_r) V_a2 tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a1 V_a2 tptp.t_a tptp.t_a) (tptp.c_Transitive__Closure_Otrancl V_r tptp.t_a) (tptp.tc_prod tptp.t_a tptp.t_a)))))))
% 2.27/2.52  (assume a393 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_b V_A T_a))) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a394 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a395 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1 V_A V_B T_b T_a) V_A T_b)))))
% 2.27/2.52  (assume a396 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1 V_A V_B T_b T_a) V_A T_b)))))
% 2.27/2.52  (assume a397 (forall ((V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 V_a V_c V_r V_s T_a T_b T_c) V_c T_c T_b) V_s (tptp.tc_prod T_c T_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_b) (tptp.c_Relation_Orel__comp V_r V_s T_a T_c T_b) (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a398 (forall ((V_a $$unsorted) (V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 V_a V_c V_r V_s T_a T_b T_c) T_a T_c) V_r (tptp.tc_prod T_a T_c))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_b) (tptp.c_Relation_Orel__comp V_r V_s T_a T_c T_b) (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a399 (forall ((T_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_COMBK V_c (tptp.tc_fun T_a tptp.tc_bool) T_b) T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a400 (forall ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_B) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.tc_fun T_a tptp.tc_bool)) V_B))))
% 2.27/2.52  (assume a401 (forall ((V_p $$unsorted) (T_a $$unsorted)) (or (= V_p (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XIdE__1__1 V_p T_a) (tptp.c_ATP__Linkup_Osko__Relation__XIdE__1__1 V_p T_a) T_a T_a)) (not (tptp.hBOOL (tptp.c_in V_p (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a402 (forall ((V_A $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_A (tptp.hAPP (tptp.c_Relation_OImage V_R T_a T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 2.27/2.52  (assume a403 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 V_r T_a) (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a404 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 V_r T_a) (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a405 (forall ((V_A $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a) V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a406 (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= V_c (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a) (tptp.c_ATP__Linkup_Osko__Relation__XId__onE__1__1 V_A V_c T_a) T_a T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a407 (forall ((V_f $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted)) (or (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_List_Osko__Recdef__Xcuts__eq__1__1 V_f V_g V_r V_x T_a T_b) V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a408 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))))
% 2.27/2.52  (assume a409 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))))
% 2.27/2.52  (assume a410 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)))))
% 2.27/2.52  (assume a411 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Relation_OId T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_r T_a) V_r T_a T_a T_a)))))
% 2.27/2.52  (assume a412 (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Orefl__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a)))
% 2.27/2.52  (assume a413 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_lessequals V_r (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 2.27/2.52  (assume a414 (= (tptp.c_Relation_ORange tptp.v_r tptp.t_a tptp.t_b) (tptp.c_Relation_ODomain (tptp.c_Relation_Oconverse tptp.v_r tptp.t_a tptp.t_b) tptp.t_b tptp.t_a)))
% 2.27/2.52  (assume a415 (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (= (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.tc_fun T_b tptp.tc_bool)) V_B)) (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) V_A) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) V_B))) (not (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Oconverse V_R T_b T_a) T_a T_b)))))
% 2.27/2.52  (assume a416 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (tptp.c_Relation_OId T_a)) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)) (not (tptp.c_Relation_Otrans V_r T_a)))))
% 2.27/2.52  (assume a417 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Nitpick_Orefl_H V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 V_r T_a) (tptp.c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a418 (forall ((V_y $$unsorted) (V_Q $$unsorted) (T_a $$unsorted) (V_R $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_y V_Q T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 V_Q V_R T_a) T_a T_a) V_R (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_x V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 2.27/2.52  (assume a419 (forall ((V_y $$unsorted) (V_Q $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_xa $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_y V_Q T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 V_Q V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_xa V_Q T_a))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a420 (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.hAPP V_f V_a) V_b) (tptp.c_Set_Oimage (tptp.c_split V_f T_a T_b T_c) V_A (tptp.tc_prod T_a T_b) T_c) T_c)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_A (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a421 (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XImageE__1__1 V_A V_b V_r T_b T_a) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a))))))
% 2.27/2.52  (assume a422 (forall ((V_A $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 V_A V_b V_r T_b T_a) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a))))))
% 2.27/2.52  (assume a423 (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__XDomainE__1__1 V_a V_r T_a T_b) T_a T_b) V_r (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))))))
% 2.27/2.52  (assume a424 (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a (tptp.c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 V_a V_r T_a T_b) T_a T_b) V_r (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))))))
% 2.27/2.52  (assume a425 (forall ((V_R $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 V_R V_x T_a) V_x T_a T_a) V_R (tptp.tc_prod T_a T_a))) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_R T_a) T_a)))))
% 2.27/2.52  (assume a426 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a427 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))))
% 2.27/2.52  (assume a428 (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 V_r V_x T_a) V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a429 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_ya $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.c_in V_ya (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_ya (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))))
% 2.27/2.52  (assume a430 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.v_sko__Wellfounded__Xacc__Xinducts__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))))
% 2.27/2.52  (assume a431 (forall ((V_P $$unsorted) (V_x $$unsorted) (V_ya $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.c_in V_ya (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_ya (tptp.v_sko__Wellfounded__Xacc__Xinduct__1 V_P V_r) tptp.t_a tptp.t_a) V_r (tptp.tc_prod tptp.t_a tptp.t_a)))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r tptp.t_a) tptp.t_a))))))
% 2.27/2.52  (assume a432 (forall ((V_P $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_a)) (tptp.hBOOL (tptp.hAPP V_P V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y (tptp.c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 V_P V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a433 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) (tptp.tc_prod T_a T_a)) V_r) T_a)))))
% 2.27/2.52  (assume a434 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.hAPP (tptp.c_Set_Oinsert (tptp.c_Pair V_y V_x T_a T_a) (tptp.tc_prod T_a T_a)) V_r) T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a435 (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XRangeE__1__1 V_b V_r T_a T_b) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_b T_a) T_a))))))
% 2.27/2.52  (assume a436 (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 V_a V_r T_a T_b) V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ORange V_r T_b T_a) T_a))))))
% 2.27/2.52  (assume a437 (forall ((V_x $$unsorted) (V_R $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 V_R V_x V_y T_a) T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a438 (forall ((V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 V_R V_x V_y T_a) V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a439 (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a440 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) V_r (tptp.tc_fun (tptp.tc_prod T_a T_a) tptp.tc_bool)) (not (tptp.c_Relation_Otrans V_r T_a)) (not (tptp.c_Relation_Osym V_r T_a)))))
% 2.27/2.52  (assume a441 (forall ((V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))))))
% 2.27/2.52  (assume a442 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) T_a))))))
% 2.27/2.52  (assume a443 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a444 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a445 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__3 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a446 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__2 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__3 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a447 (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_c $$unsorted)) (or (= (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_c (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A (tptp.c_COMBB (tptp.c_Relation_OImage V_r T_b T_a) V_B (tptp.tc_fun T_b tptp.tc_bool) (tptp.tc_fun T_a tptp.tc_bool) T_c) T_c (tptp.tc_fun T_a tptp.tc_bool))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_c tptp.tc_bool))) (not (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Oconverse V_r T_b T_a) T_a T_b)))))
% 2.27/2.52  (assume a448 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_a T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_b V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a449 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))))
% 2.27/2.52  (assume a450 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (= (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a451 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_x T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_a) (tptp.hAPP (tptp.c_Set_Oinsert V_y T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (not (tptp.hBOOL (tptp.c_in V_y V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a452 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) (tptp.tc_prod T_a T_a))) (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a453 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) (tptp.tc_prod T_a T_a)))) (= V_x V_y))))
% 2.27/2.52  (assume a454 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a455 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a456 (forall ((V_p $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_p V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a457 (forall ((V_p $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_p (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_p V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a458 (forall ((T_a $$unsorted)) (not (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))
% 2.27/2.52  (assume a459 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a460 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a)))))
% 2.27/2.52  (assume a461 (forall ((T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Relation_OId T_a) T_a)))
% 2.27/2.52  (assume a462 (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Relation_Otrans V_r T_a)))))
% 2.27/2.52  (assume a463 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Otrans V_r T_a)))))
% 2.27/2.52  (assume a464 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.c_Relation_Otrans (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 2.27/2.52  (assume a465 (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a)))
% 2.27/2.52  (assume a466 (forall ((V_r $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a)))
% 2.27/2.52  (assume a467 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Otrans (tptp.c_Relation_OId__on V_A T_a) T_a)))
% 2.27/2.52  (assume a468 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) V_r) (not (tptp.c_Relation_Otrans V_r T_a)))))
% 2.27/2.52  (assume a469 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))))
% 2.27/2.52  (assume a470 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 2.27/2.52  (assume a471 (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_r T_a)))
% 2.27/2.52  (assume a472 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a)))))
% 2.27/2.52  (assume a473 (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a474 (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a475 (forall ((V_x $$unsorted) (V_R $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Relation_ODomain V_R T_a T_a) T_a)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a476 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a)))) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Relation_ODomain V_R T_a T_a) T_a)))))
% 2.27/2.52  (assume a477 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Oirrefl V_r T_a) (not (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a)))))
% 2.27/2.52  (assume a478 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) (tptp.tc_prod T_a T_a))) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a479 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a480 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a481 (forall ((V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_z V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Osingle__valued V_r T_a T_a)))))
% 2.27/2.52  (assume a482 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a483 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a484 (forall ((V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a485 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a486 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Otrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a487 (forall ((V_f $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.hAPP (tptp.c_split V_f T_b T_c T_a) (tptp.c_Pair V_a V_b T_b T_c)) (tptp.hAPP (tptp.hAPP V_f V_a) V_b))))
% 2.27/2.52  (assume a488 (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.hAPP (tptp.c_split V_f T_a T_b T_c) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.hAPP (tptp.hAPP V_f V_a) V_b))))
% 2.27/2.52  (assume a489 (forall ((V_R $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_R V_a) V_b) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_split V_R T_a T_b (tptp.tc_fun T_c tptp.tc_bool)) (tptp.c_Pair V_a V_b T_a T_b)) V_c))))))
% 2.27/2.52  (assume a490 (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))))
% 2.27/2.52  (assume a491 (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))
% 2.27/2.52  (assume a492 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))))
% 2.27/2.52  (assume a493 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a)))))
% 2.27/2.52  (assume a494 (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))))
% 2.27/2.52  (assume a495 (forall ((V_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a))))))
% 2.27/2.52  (assume a496 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_a V_A T_b))) (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a))))))
% 2.27/2.52  (assume a497 (forall ((V_b $$unsorted) (V_B $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_x) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) T_a))))))
% 2.27/2.52  (assume a498 (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))
% 2.27/2.52  (assume a499 (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))
% 2.27/2.52  (assume a500 (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))))
% 2.27/2.52  (assume a501 (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))
% 2.27/2.52  (assume a502 (forall ((V_B $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b))))))
% 2.27/2.52  (assume a503 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_b $$unsorted) (T_b $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b))))))
% 2.27/2.52  (assume a504 (forall ((V_B $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b))))))
% 2.27/2.52  (assume a505 (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a506 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osingle__valued (tptp.c_Relation_OId__on V_A T_a) T_a T_a)))
% 2.27/2.52  (assume a507 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))))
% 2.27/2.52  (assume a508 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym V_r T_a) (not (tptp.c_Relation_Osym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 2.27/2.52  (assume a509 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))))
% 2.27/2.52  (assume a510 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a511 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ODomain V_r T_a T_a))))
% 2.27/2.52  (assume a512 (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))))
% 2.27/2.52  (assume a513 (forall ((T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Relation_OId T_a) T_a)))
% 2.27/2.52  (assume a514 (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))))
% 2.27/2.52  (assume a515 (forall ((T_a $$unsorted) (V_R $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_OId T_a) V_R T_a T_a T_b) V_R)))
% 2.27/2.52  (assume a516 (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_R (tptp.c_Relation_OId T_b) T_a T_b T_b) V_R)))
% 2.27/2.52  (assume a517 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Oantisym (tptp.c_Relation_OId__on V_A T_a) T_a)))
% 2.27/2.52  (assume a518 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 2.27/2.52  (assume a519 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A V_r T_a) (not (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 2.27/2.52  (assume a520 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 2.27/2.52  (assume a521 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (not (tptp.c_Relation_Osym V_r T_a)))))
% 2.27/2.52  (assume a522 (forall ((V_R $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) T_a) (not (tptp.c_Wellfounded_Owf V_R T_a)))))
% 2.27/2.52  (assume a523 (forall ((V_R $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf V_R T_a) (not (tptp.c_Wellfounded_Owf (tptp.c_Relation_Orel__comp V_R V_R T_a T_a T_a) T_a)))))
% 2.27/2.52  (assume a524 (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage (tptp.c_Relation_OId T_a) T_a T_a) V_A) V_A)))
% 2.27/2.52  (assume a525 (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a526 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_OId T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a527 (forall ((T_a $$unsorted)) (tptp.c_Relation_Osingle__valued (tptp.c_Relation_OId T_a) T_a T_a)))
% 2.27/2.52  (assume a528 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 V_A V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 V_A V_r T_a))) (tptp.c_Relation_Ototal__on V_A V_r T_a))))
% 2.27/2.52  (assume a529 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)))
% 2.27/2.52  (assume a530 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Relation_Oconverse V_r T_a T_a) V_r) (not (tptp.c_Relation_Osym V_r T_a)))))
% 2.27/2.52  (assume a531 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Relation_Oconverse V_r T_a T_a) V_r)) (tptp.c_Relation_Osym V_r T_a))))
% 2.27/2.52  (assume a532 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ORange V_r T_a T_a))))
% 2.27/2.52  (assume a533 (forall ((V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Orel__comp V_r V_s T_b T_c T_a) T_b T_a) (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_s T_c T_a) (tptp.c_Relation_Oconverse V_r T_b T_c) T_a T_c T_b))))
% 2.27/2.52  (assume a534 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Osym (tptp.c_Relation_OId__on V_A T_a) T_a)))
% 2.27/2.52  (assume a535 (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_OId__on V_A T_a) T_a)))
% 2.27/2.52  (assume a536 (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a537 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_OId T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a538 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp V_r (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a T_a T_a) (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_r T_a) V_r T_a T_a T_a))))
% 2.27/2.52  (assume a539 (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))))
% 2.27/2.52  (assume a540 (forall ((V_r $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Relation_Osym (tptp.c_Relation_Oinv__image V_r V_f T_a T_b) T_b) (not (tptp.c_Relation_Osym V_r T_a)))))
% 2.27/2.52  (assume a541 (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))
% 2.27/2.52  (assume a542 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 2.27/2.52  (assume a543 (forall ((T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_OId T_a) T_a T_a) (tptp.c_Relation_OId T_a))))
% 2.27/2.52  (assume a544 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Wellfounded_Owf (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a545 (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Relation_OImage V_R T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a546 (forall ((V_R $$unsorted) (V_S $$unsorted) (T_a $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (V_T $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Orel__comp V_R V_S T_a T_d T_c) V_T T_a T_c T_b) (tptp.c_Relation_Orel__comp V_R (tptp.c_Relation_Orel__comp V_S V_T T_d T_c T_b) T_a T_d T_b))))
% 2.27/2.52  (assume a547 (forall ((V_R $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oinv__image V_R V_f T_b T_a) T_a T_a) (tptp.c_Relation_Oinv__image (tptp.c_Relation_Oconverse V_R T_b T_b) V_f T_b T_a))))
% 2.27/2.52  (assume a548 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a))))
% 2.27/2.52  (assume a549 (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))))
% 2.27/2.52  (assume a550 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_OId__on V_A T_a) T_a T_a) (tptp.c_Relation_OId__on V_A T_a))))
% 2.27/2.52  (assume a551 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) V_r)) (tptp.c_Equiv__Relations_Oequiv (tptp.c_Relation_ODomain V_r T_a T_a) V_r T_a))))
% 2.27/2.52  (assume a552 (forall ((T_a $$unsorted)) (tptp.c_Relation_Oantisym (tptp.c_Relation_OId T_a) T_a)))
% 2.27/2.52  (assume a553 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) (tptp.c_Relation_ODomain V_r T_a T_b))))
% 2.27/2.52  (assume a554 (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)))
% 2.27/2.52  (assume a555 (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (or (tptp.c_Relation_Osingle__valued (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) T_a T_c) (not (tptp.c_Relation_Osingle__valued V_s T_b T_c)) (not (tptp.c_Relation_Osingle__valued V_r T_a T_b)))))
% 2.27/2.52  (assume a556 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) V_r)))
% 2.27/2.52  (assume a557 (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Orefl__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a)))
% 2.27/2.52  (assume a558 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Relation_Orel__comp (tptp.c_Relation_Oconverse V_r T_a T_a) V_r T_a T_a T_a) V_r) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a559 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 2.27/2.52  (assume a560 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym V_r T_a) (not (tptp.c_Relation_Oantisym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)))))
% 2.27/2.52  (assume a561 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oantisym (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (not (tptp.c_Relation_Oantisym V_r T_a)))))
% 2.27/2.52  (assume a562 (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))))
% 2.27/2.52  (assume a563 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a564 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a565 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Relation_Oconverse V_r T_a T_a) T_a) (tptp.c_Relation_Oconverse (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a T_a))))
% 2.27/2.52  (assume a566 (forall ((T_a $$unsorted)) (tptp.c_Relation_Orefl__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Relation_OId T_a) T_a)))
% 2.27/2.52  (assume a567 (forall ((V_r $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_Relation_Osym V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a568 (forall ((T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))))
% 2.27/2.52  (assume a569 (forall ((V_r2 $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_r1 $$unsorted)) (or (tptp.c_Equiv__Relations_Ocongruent V_r2 (tptp.hAPP V_f V_a) T_b T_c) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Equiv__Relations_Ocongruent2 V_r1 V_r2 V_f T_a T_b T_c)) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r1 T_a)))))
% 2.27/2.52  (assume a570 (forall ((V_P $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xb)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 V_P T_a)))))))
% 2.27/2.52  (assume a571 (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_Oconverse V_r T_b T_a) T_a T_b) (tptp.c_Relation_ORange V_r T_b T_a))))
% 2.27/2.52  (assume a572 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_Orel__comp (tptp.c_Transitive__Closure_Ortrancl V_r T_a) V_r T_a T_a T_a))))
% 2.27/2.52  (assume a573 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.c_Relation_Orel__comp V_r (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a T_a T_a))))
% 2.27/2.52  (assume a574 (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))))
% 2.27/2.52  (assume a575 (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange V_r T_b T_a) (tptp.c_Relation_ODomain (tptp.c_Relation_Oconverse V_r T_b T_a) T_a T_b))))
% 2.27/2.52  (assume a576 (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Transitive__Closure_Otrancl V_R T_a) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))))
% 2.27/2.52  (assume a577 (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_Transitive__Closure_Ortrancl V_r T_a) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))))
% 2.27/2.52  (assume a578 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a579 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a580 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__XtransI__1__2 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a581 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Otrans V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a582 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 V_A V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 V_A V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a583 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 V_A V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 V_A V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a584 (forall ((V_z $$unsorted) (V_c $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_z (tptp.hAPP (tptp.c_split V_c T_b T_c (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Pair V_a V_b T_b T_c)) T_a)) (not (tptp.hBOOL (tptp.c_in V_z (tptp.hAPP (tptp.hAPP V_c V_a) V_b) T_a))))))
% 2.27/2.52  (assume a585 (forall ((V_f $$unsorted) (V_y1 $$unsorted) (V_y2 $$unsorted) (V_z1 $$unsorted) (V_z2 $$unsorted) (T_b $$unsorted) (V_r2 $$unsorted) (T_a $$unsorted) (V_r1 $$unsorted) (T_c $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_f V_y1) V_y2) (tptp.hAPP (tptp.hAPP V_f V_z1) V_z2)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y2 V_z2 T_b T_b) V_r2 (tptp.tc_prod T_b T_b)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y1 V_z1 T_a T_a) V_r1 (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Ocongruent2 V_r1 V_r2 V_f T_a T_b T_c)))))
% 2.27/2.52  (assume a586 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (= V_y V_z) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_b) V_r (tptp.tc_prod T_a T_b)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_b) V_r (tptp.tc_prod T_a T_b)))) (not (tptp.c_Relation_Osingle__valued V_r T_a T_b)))))
% 2.27/2.52  (assume a587 (forall ((V_f $$unsorted) (V_R $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Recdef_Ocut V_f V_R V_a T_a T_b) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_a T_a) V_R (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a588 (forall ((V_f $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (= (tptp.hAPP (tptp.c_Recdef_Ocut V_f V_r V_a T_a T_b) V_x) (tptp.hAPP V_f V_x)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a589 (forall ((V_R $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_FunDef_Oin__rel V_R V_x V_y T_a T_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_b) V_R (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a590 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_b) V_R (tptp.tc_prod T_a T_b))) (not (tptp.c_FunDef_Oin__rel V_R V_x V_y T_a T_b)))))
% 2.27/2.52  (assume a591 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a)))))))
% 2.27/2.52  (assume a592 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) (tptp.c_Relation_Oconverse V_r T_a T_b) (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a593 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a594 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a595 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a596 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a597 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a598 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a599 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a600 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a)))))
% 2.27/2.52  (assume a601 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a) (tptp.tc_prod T_a T_a)))))
% 2.27/2.52  (assume a602 (forall ((V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a603 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oantisym V_r T_a)))))
% 2.27/2.52  (assume a604 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oantisym V_r T_a)))))
% 2.27/2.52  (assume a605 (forall ((V_f $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_f V_y) (tptp.hAPP V_f V_z)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Ocongruent V_r V_f T_a T_b)))))
% 2.27/2.52  (assume a606 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a607 (forall ((V_f $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Recdef_Ocut V_f V_r V_x T_a T_b) (tptp.c_Recdef_Ocut V_g V_r V_x T_a T_b))) (= (tptp.hAPP V_f V_y) (tptp.hAPP V_g V_y)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a608 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (= V_a V_b) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a609 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.c_Nitpick_Orefl_H V_r T_a)))))
% 2.27/2.52  (assume a610 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Wellfounded_Owf V_r T_a)))))
% 2.27/2.52  (assume a611 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_Oinv__image V_r V_f T_b T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b T_b) V_r (tptp.tc_prod T_b T_b)))))))
% 2.27/2.52  (assume a612 (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b T_b) V_r (tptp.tc_prod T_b T_b))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_Oinv__image V_r V_f T_b T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a613 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Osym V_r T_a)))))
% 2.27/2.52  (assume a614 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_a T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Osym V_r T_a)))))
% 2.27/2.52  (assume a615 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_c) (tptp.c_Relation_Orel__comp V_r V_s T_a T_b T_c) (tptp.tc_prod T_a T_c))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_b T_c) V_s (tptp.tc_prod T_b T_c)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a616 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_R T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_R (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_R (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a617 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) (tptp.c_Transitive__Closure_Otrancl V_r T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a618 (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))))
% 2.27/2.52  (assume a619 (forall ((V_a $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Relation_OId T_a) (tptp.tc_prod T_a T_a)))))
% 2.27/2.52  (assume a620 (forall ((T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1 T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))))
% 2.27/2.52  (assume a621 (forall ((V_P $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1 V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.c_in V_xa (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))))))
% 2.27/2.52  (assume a622 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP V_B V_x) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))
% 2.27/2.52  (assume a623 (forall ((V_P $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 V_P T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))))
% 2.27/2.52  (assume a624 (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_A) (not (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1 V_A T_a) V_A T_a))))))
% 2.27/2.52  (assume a625 (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2 V_P T_a)))))))
% 2.27/2.52  (assume a626 (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a))))
% 2.27/2.52  (assume a627 (forall ((V_P $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_xa)) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 V_P T_a) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))
% 2.27/2.52  (assume a628 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OINFI V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.hAPP V_B V_x) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))
% 2.27/2.52  (assume a629 (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)) tptp.v_x) (tptp.c_in tptp.v_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)) tptp.t_a)))
% 2.27/2.52  (assume a630 (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))))
% 2.27/2.52  (assume a631 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_L (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_x V_y) (= V_x V_z))))
% 2.27/2.52  (assume a632 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_L (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_y V_z) (= V_x V_z))))
% 2.27/2.52  (assume a633 (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))))
% 2.27/2.52  (assume a634 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))))
% 2.27/2.52  (assume a635 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_L (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= V_y V_z) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))))))
% 2.27/2.52  (assume a636 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (or (= V_x V_y) (= V_y V_x) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))))
% 2.27/2.52  (assume a637 (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))))
% 2.27/2.52  (assume a638 (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))))
% 2.27/2.52  (assume a639 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_L (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_x V_y) (= V_y V_z))))
% 2.27/2.52  (assume a640 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_L (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_x V_z) (= V_y V_z))))
% 2.27/2.52  (assume a641 (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (or (= V_xa V_x) (= V_xa V_x) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))))
% 2.27/2.52  (assume a642 (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) V_L (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= V_x V_z) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))))))
% 2.27/2.52  (assume a643 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 V_A V_r T_a) V_A T_a)))))
% 2.27/2.52  (assume a644 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Ototal__on V_A V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 V_A V_r T_a) V_A T_a)))))
% 2.27/2.52  (assume a645 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))
% 2.27/2.52  (assume a646 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))
% 2.27/2.52  (assume a647 (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_b (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a648 (forall ((V_y $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_y (tptp.c_Wellfounded_Oacc V_r T_a) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_a T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Wellfounded_Oacc V_r T_a) T_a))))))
% 2.27/2.52  (assume a649 (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_a T_b) V_A) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))
% 2.27/2.52  (assume a650 (forall ((V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP (tptp.c_Relation_OImage V_r T_b T_a) V_A) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))))
% 2.27/2.52  (assume a651 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a)))))))
% 2.27/2.52  (assume a652 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) (tptp.c_Relation_OId__on V_A T_a) (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))))
% 2.27/2.52  (assume a653 (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_y V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a654 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))))
% 2.27/2.52  (assume a655 (forall ((V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ORange V_r T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_a T_b T_a) V_r (tptp.tc_prod T_b T_a)))))))
% 2.27/2.52  (assume a656 (forall ((V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_a T_b) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a657 (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_x T_a T_b) V_r (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a658 (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a659 (forall ((V_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_b (tptp.hAPP V_B V_a) T_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a660 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b) (tptp.tc_prod T_a T_b)))))))
% 2.27/2.52  (assume a661 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 2.27/2.52  (assume a662 (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_y V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 2.27/2.52  (assume a663 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 2.27/2.52  (assume a664 (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))))
% 2.27/2.52  (assume a665 (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Oirrefl V_r T_a) (tptp.hBOOL (tptp.c_in (tptp.c_Pair (tptp.c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 V_r T_a) (tptp.c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 V_r T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))))
% 2.27/2.52  (assume a666 (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Order__Relation_Ostrict__linear__order__on V_A V_r T_a) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)) (not (tptp.c_Relation_Oirrefl V_r T_a)) (not (tptp.c_Relation_Otrans V_r T_a)))))
% 2.27/2.52  (assume a667 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_b V_b_H))))
% 2.27/2.52  (assume a668 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_a V_a_H))))
% 2.27/2.52  (assume a669 (forall ((V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_z T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_y V_z T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Otrans V_r T_a)))))
% 2.27/2.52  (assume a670 (forall ((V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_c T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_b V_c T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Otrans V_r T_a)))))
% 2.27/2.52  (assume a671 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))))
% 2.27/2.52  (assume a672 (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))))
% 2.27/2.52  (assume a673 (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))))
% 2.27/2.52  (assume a674 (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))))
% 2.27/2.52  (assume a675 (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_xa V_x T_a T_a) V_r (tptp.tc_prod T_a T_a))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_xa T_a T_a) V_r (tptp.tc_prod T_a T_a))) (= V_x V_xa) (not (tptp.hBOOL (tptp.c_in V_xa V_A T_a))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))))
% 2.27/2.52  (assume a676 (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_S T_a)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))))
% 2.27/2.52  (assume a677 (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_S T_a))))))
% 2.27/2.52  (assume a678 (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.52  (assume a679 (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.52  (assume a680 (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.52  (assume a681 (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))
% 2.27/2.52  (assume a682 (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))))
% 2.27/2.52  (assume a683 (forall ((V_xa $$unsorted)) (or (tptp.c_Relation_Otrans (tptp.v_F V_xa) tptp.tc_Arrow__Order__Mirabelle_Oalt) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_xa (tptp.hAPP tptp.v_x V_xa)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_xa (tptp.hAPP tptp.v_x V_xa)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_xa (tptp.hAPP tptp.v_x V_xa)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))))
% 2.27/2.52  (assume a684 (forall ((V_xa $$unsorted)) (or (tptp.c_Relation_Oirrefl (tptp.v_F V_xa) tptp.tc_Arrow__Order__Mirabelle_Oalt) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_xa (tptp.hAPP tptp.v_x V_xa)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_xa (tptp.hAPP tptp.v_x V_xa)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_xa (tptp.hAPP tptp.v_x V_xa)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))))
% 2.27/2.52  (assume a685 (forall ((V_xa $$unsorted)) (or (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.v_F V_xa) tptp.tc_Arrow__Order__Mirabelle_Oalt) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_xa (tptp.hAPP tptp.v_x V_xa)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_xa (tptp.hAPP tptp.v_x V_xa)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_xa (tptp.hAPP tptp.v_x V_xa)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))))
% 2.27/2.52  (assume a686 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))))
% 2.27/2.52  (assume a687 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))))
% 2.27/2.52  (assume a688 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))))
% 2.27/2.52  (assume a689 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))))
% 2.27/2.52  (assume a690 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice T_1)))))
% 2.27/2.52  (assume a691 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))))
% 2.27/2.52  (assume a692 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))))
% 2.27/2.52  (assume a693 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))))
% 2.27/2.52  (assume a694 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))))
% 2.27/2.52  (assume a695 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))))
% 2.27/2.52  (assume a696 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))))
% 2.27/2.52  (assume a697 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ominus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ominus T_1)))))
% 2.27/2.52  (assume a698 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))))
% 2.27/2.52  (assume a699 (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool))
% 2.27/2.52  (assume a700 (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool))
% 2.27/2.52  (assume a701 (tptp.class_Lattices_Olower__semilattice tptp.tc_bool))
% 2.27/2.52  (assume a702 (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool))
% 2.27/2.52  (assume a703 (tptp.class_Lattices_Obounded__lattice tptp.tc_bool))
% 2.27/2.52  (assume a704 (tptp.class_Orderings_Opreorder tptp.tc_bool))
% 2.27/2.52  (assume a705 (tptp.class_Lattices_Olattice tptp.tc_bool))
% 2.27/2.52  (assume a706 (tptp.class_Orderings_Oorder tptp.tc_bool))
% 2.27/2.52  (assume a707 (tptp.class_Orderings_Otop tptp.tc_bool))
% 2.27/2.52  (assume a708 (tptp.class_Orderings_Obot tptp.tc_bool))
% 2.27/2.52  (assume a709 (tptp.class_HOL_Ominus tptp.tc_bool))
% 2.27/2.52  (assume a710 (tptp.class_HOL_Oord tptp.tc_bool))
% 2.27/2.52  (assume a711 (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)))
% 2.27/2.52  (assume a712 (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a)))))
% 2.27/2.52  (step t1 (cl (=> (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a))))) :rule implies_neg1)
% 2.27/2.52  (anchor :step t2)
% 2.27/2.52  (assume t2.a0 (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))))
% 2.27/2.52  (step t2.t1 (cl (or (not (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a))))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule forall_inst :args ((:= V_x tptp.v_a) (:= T_a tptp.tc_Arrow__Order__Mirabelle_Oalt) (:= V_r (tptp.hAPP tptp.v_P tptp.v_i))))
% 2.27/2.52  (step t2.t2 (cl (not (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a))))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule or :premises (t2.t1))
% 2.27/2.52  (step t2.t3 (cl (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t2.t2 t2.a0))
% 2.27/2.52  (step t2 (cl (not (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a))))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule subproof :discharge (t2.a0))
% 2.27/2.52  (step t3 (cl (=> (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t1 t2))
% 2.27/2.52  (step t4 (cl (=> (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule implies_neg2)
% 2.27/2.52  (step t5 (cl (=> (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (=> (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule resolution :premises (t3 t4))
% 2.27/2.52  (step t6 (cl (=> (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a)))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule contraction :premises (t5))
% 2.27/2.52  (step t7 (cl (not (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)))) (not (tptp.c_Relation_Oirrefl V_r T_a))))) (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule implies :premises (t6))
% 2.27/2.52  (step t8 (cl (not (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule or_pos)
% 2.27/2.52  (step t9 (cl (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule reordering :premises (t8))
% 2.27/2.52  (step t10 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule implies_neg1)
% 2.27/2.52  (anchor :step t11)
% 2.27/2.52  (assume t11.a0 (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.52  (step t11.t1 (cl (or (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule forall_inst :args ((:= V_x tptp.v_i)))
% 2.27/2.52  (step t11.t2 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule or :premises (t11.t1))
% 2.27/2.52  (step t11.t3 (cl (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t11.t2 t11.a0))
% 2.27/2.52  (step t11 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule subproof :discharge (t11.a0))
% 2.27/2.52  (step t12 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t10 t11))
% 2.27/2.52  (step t13 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule implies_neg2)
% 2.27/2.52  (step t14 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule resolution :premises (t12 t13))
% 2.27/2.52  (step t15 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule contraction :premises (t14))
% 2.27/2.52  (step t16 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule implies :premises (t15))
% 2.27/2.52  (step t17 (cl (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t16 a679))
% 2.27/2.52  (step t18 (cl (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (= tptp.v_a tptp.v_b)) (not (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule and_neg)
% 2.27/2.52  (step t19 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule implies_neg1)
% 2.27/2.52  (anchor :step t20)
% 2.27/2.52  (assume t20.a0 (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))
% 2.27/2.52  (assume t20.a1 (= tptp.v_a tptp.v_b))
% 2.27/2.52  (assume t20.a2 (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.52  (step t20.t1 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) :rule implies_neg1)
% 2.27/2.52  (anchor :step t20.t2)
% 2.27/2.52  (assume t20.t2.a0 (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))
% 2.27/2.52  (assume t20.t2.a1 (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.52  (assume t20.t2.a2 (= tptp.v_a tptp.v_b))
% 2.27/2.52  (step t20.t2.t1 (cl (= (= (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) true) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule equiv_simplify)
% 2.27/2.52  (step t20.t2.t2 (cl (not (= (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) true)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule equiv1 :premises (t20.t2.t1))
% 2.27/2.52  (step t20.t2.t3 (cl (= tptp.v_a tptp.v_a)) :rule refl)
% 2.27/2.53  (step t20.t2.t4 (cl (= tptp.v_b tptp.v_a)) :rule symm :premises (t20.t2.a2))
% 2.27/2.53  (step t20.t2.t5 (cl (= tptp.v_a tptp.v_b)) :rule symm :premises (t20.t2.t4))
% 2.27/2.53  (step t20.t2.t6 (cl (= tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule refl)
% 2.27/2.53  (step t20.t2.t7 (cl (= (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule cong :premises (t20.t2.t3 t20.t2.t5 t20.t2.t6 t20.t2.t6))
% 2.27/2.53  (step t20.t2.t8 (cl (= (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule refl)
% 2.27/2.53  (step t20.t2.t9 (cl (= (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule cong :premises (t20.t2.t7 t20.t2.a1 t20.t2.t8))
% 2.27/2.53  (step t20.t2.t10 (cl (= (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule refl)
% 2.27/2.53  (step t20.t2.t11 (cl (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i))) :rule symm :premises (t20.t2.a1))
% 2.27/2.53  (step t20.t2.t12 (cl (= (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule cong :premises (t20.t2.t10 t20.t2.t11 t20.t2.t8))
% 2.27/2.53  (step t20.t2.t13 (cl (= (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule trans :premises (t20.t2.t9 t20.t2.t12))
% 2.27/2.53  (step t20.t2.t14 (cl (= (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule cong :premises (t20.t2.t13))
% 2.27/2.53  (step t20.t2.t15 (cl (= (= (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) true) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule equiv_simplify)
% 2.27/2.53  (step t20.t2.t16 (cl (= (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) true) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule equiv2 :premises (t20.t2.t15))
% 2.27/2.53  (step t20.t2.t17 (cl (= (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) true)) :rule resolution :premises (t20.t2.t16 t20.t2.a0))
% 2.27/2.53  (step t20.t2.t18 (cl (= (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) true)) :rule trans :premises (t20.t2.t14 t20.t2.t17))
% 2.27/2.53  (step t20.t2.t19 (cl (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t20.t2.t2 t20.t2.t18))
% 2.27/2.53  (step t20.t2 (cl (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (= tptp.v_a tptp.v_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule subproof :discharge (t20.t2.a0 t20.t2.a1 t20.t2.a2))
% 2.27/2.53  (step t20.t3 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule and_pos)
% 2.27/2.53  (step t20.t4 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule and_pos)
% 2.27/2.53  (step t20.t5 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (= tptp.v_a tptp.v_b)) :rule and_pos)
% 2.27/2.53  (step t20.t6 (cl (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b)))) :rule resolution :premises (t20.t2 t20.t3 t20.t4 t20.t5))
% 2.27/2.53  (step t20.t7 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule reordering :premises (t20.t6))
% 2.27/2.53  (step t20.t8 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule contraction :premises (t20.t7))
% 2.27/2.53  (step t20.t9 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t20.t1 t20.t8))
% 2.27/2.53  (step t20.t10 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule implies_neg2)
% 2.27/2.53  (step t20.t11 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule resolution :premises (t20.t9 t20.t10))
% 2.27/2.53  (step t20.t12 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule contraction :premises (t20.t11))
% 2.27/2.53  (step t20.t13 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule implies :premises (t20.t12))
% 2.27/2.53  (step t20.t14 (cl (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (= tptp.v_a tptp.v_b))) :rule and_neg)
% 2.27/2.53  (step t20.t15 (cl (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (= tptp.v_a tptp.v_b))) :rule resolution :premises (t20.t14 t20.a0 t20.a2 t20.a1))
% 2.27/2.53  (step t20.t16 (cl (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t20.t13 t20.t15))
% 2.27/2.53  (step t20 (cl (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (= tptp.v_a tptp.v_b)) (not (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule subproof :discharge (t20.a0 t20.a1 t20.a2))
% 2.27/2.53  (step t21 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule and_pos)
% 2.27/2.53  (step t22 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b)) :rule and_pos)
% 2.27/2.53  (step t23 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule and_pos)
% 2.27/2.53  (step t24 (cl (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule resolution :premises (t20 t21 t22 t23))
% 2.27/2.53  (step t25 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule reordering :premises (t24))
% 2.27/2.53  (step t26 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule contraction :premises (t25))
% 2.27/2.53  (step t27 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t19 t26))
% 2.27/2.53  (step t28 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule implies_neg2)
% 2.27/2.53  (step t29 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule resolution :premises (t27 t28))
% 2.27/2.53  (step t30 (cl (=> (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule contraction :premises (t29))
% 2.27/2.53  (step t31 (cl (not (and (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= tptp.v_a tptp.v_b) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule implies :premises (t30))
% 2.27/2.53  (step t32 (cl (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (= tptp.v_a tptp.v_b)) (not (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t18 t31))
% 2.27/2.53  (step t33 (cl (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (= tptp.v_a tptp.v_b)) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule reordering :premises (t32))
% 2.27/2.53  (step t34 (cl (not (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule or_pos)
% 2.27/2.53  (step t35 (cl (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule reordering :premises (t34))
% 2.27/2.53  (step t36 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule implies_neg1)
% 2.27/2.53  (anchor :step t37)
% 2.27/2.53  (assume t37.a0 (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.53  (step t37.t1 (cl (or (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule forall_inst :args ((:= V_x (tptp.v_Pa tptp.v_P))))
% 2.27/2.53  (step t37.t2 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule or :premises (t37.t1))
% 2.27/2.53  (step t37.t3 (cl (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t37.t2 t37.a0))
% 2.27/2.53  (step t37 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule subproof :discharge (t37.a0))
% 2.27/2.53  (step t38 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t36 t37))
% 2.27/2.53  (step t39 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule implies_neg2)
% 2.27/2.53  (step t40 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule resolution :premises (t38 t39))
% 2.27/2.53  (step t41 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule contraction :premises (t40))
% 2.27/2.53  (step t42 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule implies :premises (t41))
% 2.27/2.53  (step t43 (cl (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t42 a680))
% 2.27/2.53  (step t44 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule implies_neg1)
% 2.27/2.53  (anchor :step t45)
% 2.27/2.53  (assume t45.a0 (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.53  (step t45.t1 (cl (or (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule forall_inst :args ((:= V_x (tptp.v_Pa tptp.v_P))))
% 2.27/2.53  (step t45.t2 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule or :premises (t45.t1))
% 2.27/2.53  (step t45.t3 (cl (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t45.t2 t45.a0))
% 2.27/2.53  (step t45 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule subproof :discharge (t45.a0))
% 2.27/2.53  (step t46 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t44 t45))
% 2.27/2.53  (step t47 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule implies_neg2)
% 2.27/2.53  (step t48 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule resolution :premises (t46 t47))
% 2.27/2.53  (step t49 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule contraction :premises (t48))
% 2.27/2.53  (step t50 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule implies :premises (t49))
% 2.27/2.53  (step t51 (cl (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t50 a679))
% 2.27/2.53  (step t52 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule implies_neg1)
% 2.27/2.53  (anchor :step t53)
% 2.27/2.53  (assume t53.a0 (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.53  (step t53.t1 (cl (or (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule forall_inst :args ((:= V_x (tptp.v_Pa tptp.v_P))))
% 2.27/2.53  (step t53.t2 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule or :premises (t53.t1))
% 2.27/2.53  (step t53.t3 (cl (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t53.t2 t53.a0))
% 2.27/2.53  (step t53 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule subproof :discharge (t53.a0))
% 2.27/2.53  (step t54 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t52 t53))
% 2.27/2.53  (step t55 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule implies_neg2)
% 2.27/2.53  (step t56 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule resolution :premises (t54 t55))
% 2.27/2.53  (step t57 (cl (=> (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule contraction :premises (t56))
% 2.27/2.53  (step t58 (cl (not (forall ((V_x $$unsorted)) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P V_x) tptp.tc_Arrow__Order__Mirabelle_Oalt))) (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule implies :premises (t57))
% 2.27/2.53  (step t59 (cl (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) :rule resolution :premises (t58 a678))
% 2.27/2.53  (step t60 (cl (=> (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule implies_neg1)
% 2.27/2.53  (anchor :step t61)
% 2.27/2.53  (assume t61.a0 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))))
% 2.27/2.53  (step t61.t1 (cl (or (not (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule forall_inst :args ((:= V_a tptp.v_a) (:= V_b tptp.v_b) (:= V_P tptp.v_P)))
% 2.27/2.53  (step t61.t2 (cl (not (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule or :premises (t61.t1))
% 2.27/2.53  (step t61.t3 (cl (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t61.t2 t61.a0))
% 2.27/2.53  (step t61 (cl (not (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule subproof :discharge (t61.a0))
% 2.27/2.53  (step t62 (cl (=> (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t60 t61))
% 2.27/2.53  (step t63 (cl (=> (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule implies_neg2)
% 2.27/2.53  (step t64 (cl (=> (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (=> (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule resolution :premises (t62 t63))
% 2.27/2.53  (step t65 (cl (=> (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule contraction :premises (t64))
% 2.27/2.53  (step t66 (cl (not (forall ((V_a $$unsorted) (V_b $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F V_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP V_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= V_a V_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP V_P (tptp.v_Pa V_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule implies :premises (t65))
% 2.27/2.53  (step t67 (cl (or (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.v_F tptp.v_P) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (= tptp.v_a tptp.v_b) (not (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_bool)) (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)) (not (tptp.c_Relation_Otrans (tptp.hAPP tptp.v_P (tptp.v_Pa tptp.v_P)) tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t66 a686))
% 2.27/2.53  (step t68 (cl (= tptp.v_a tptp.v_b)) :rule resolution :premises (t35 a682 a681 t43 t51 t59 t67))
% 2.27/2.53  (step t69 (cl (=> (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a)))) :rule implies_neg1)
% 2.27/2.53  (anchor :step t70)
% 2.27/2.53  (assume t70.a0 (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a))))
% 2.27/2.53  (step t70.t1 (cl (or (not (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a)))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule forall_inst :args ((:= V_r (tptp.hAPP tptp.v_P tptp.v_i)) (:= T_a tptp.tc_Arrow__Order__Mirabelle_Oalt) (:= T_b tptp.tc_Arrow__Order__Mirabelle_Oalt)))
% 2.27/2.53  (step t70.t2 (cl (not (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a)))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule or :premises (t70.t1))
% 2.27/2.53  (step t70.t3 (cl (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule resolution :premises (t70.t2 t70.a0))
% 2.27/2.53  (step t70 (cl (not (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a)))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule subproof :discharge (t70.a0))
% 2.27/2.53  (step t71 (cl (=> (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule resolution :premises (t69 t70))
% 2.27/2.53  (step t72 (cl (=> (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (not (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule implies_neg2)
% 2.27/2.53  (step t73 (cl (=> (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (=> (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t71 t72))
% 2.27/2.53  (step t74 (cl (=> (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule contraction :premises (t73))
% 2.27/2.53  (step t75 (cl (not (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a)))) (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule implies :premises (t74))
% 2.27/2.53  (step t76 (cl (not (= (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) V_r)) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a))))) (not (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) V_r))) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a)))) :rule equiv_pos2)
% 2.27/2.53  (anchor :step t77 :args ((V_r $$unsorted) (:= V_r V_r) (T_a $$unsorted) (:= T_a T_a) (T_b $$unsorted) (:= T_b T_b)))
% 2.27/2.53  (step t77.t1 (cl (= V_r V_r)) :rule refl)
% 2.27/2.53  (step t77.t2 (cl (= T_a T_a)) :rule refl)
% 2.27/2.53  (step t77.t3 (cl (= T_b T_b)) :rule refl)
% 2.27/2.53  (step t77.t4 (cl (= (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) V_r) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a)))) :rule all_simplify)
% 2.27/2.53  (step t77 (cl (= (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a) V_r)) (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a))))) :rule bind)
% 2.27/2.53  (step t78 (cl (forall ((V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_r (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_r T_a T_b) T_b T_a)))) :rule resolution :premises (t76 t77 a556))
% 2.27/2.53  (step t79 (cl (= (tptp.hAPP tptp.v_P tptp.v_i) (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) :rule resolution :premises (t75 t78))
% 2.27/2.53  (step t80 (cl (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) :rule resolution :premises (t33 a681 t68 t79))
% 2.27/2.53  (step t81 (cl (not (or (not (tptp.hBOOL (tptp.c_in (tptp.c_Pair tptp.v_a tptp.v_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) (tptp.hAPP tptp.v_P tptp.v_i) (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (not (tptp.c_Relation_Oirrefl (tptp.hAPP tptp.v_P tptp.v_i) tptp.tc_Arrow__Order__Mirabelle_Oalt))))) :rule resolution :premises (t9 t17 t80))
% 2.27/2.53  (step t82 (cl) :rule resolution :premises (t7 t81 a671))
% 2.27/2.53  
% 2.36/2.53  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.Fpm6wbrBOy/cvc5---1.0.5_13943.smt2
% 2.36/2.54  % cvc5---1.0.5 exiting
% 2.36/2.54  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------