TSTP Solution File: SWW473+6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW473+6 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n010.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 18:20:00 EDT 2024
% Result : Theorem 10.23s 10.45s
% Output : Proof 10.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.23 % Problem : SWW473+6 : TPTP v8.2.0. Released v5.3.0.
% 0.12/0.24 % Command : do_cvc5 %s %d
% 0.24/0.45 % Computer : n010.cluster.edu
% 0.24/0.45 % Model : x86_64 x86_64
% 0.24/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.45 % Memory : 8042.1875MB
% 0.24/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.24/0.45 % CPULimit : 300
% 0.24/0.45 % WCLimit : 300
% 0.24/0.45 % DateTime : Sun May 26 04:48:39 EDT 2024
% 0.24/0.45 % CPUTime :
% 0.53/0.88 %----Proving TF0_NAR, FOF, or CNF
% 10.23/10.45 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.23/10.45 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.SVwWjdnxnN/cvc5---1.0.5_24393.smt2
% 10.23/10.45 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.SVwWjdnxnN/cvc5---1.0.5_24393.smt2
% 10.23/10.45 (assume a0 (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) (tptp.combb X_b X_c X_a)) (tptp.combb X_b X_c X_a))))
% 10.23/10.45 (assume a1 (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun X_b (tptp.fun X_a X_c))) (tptp.combc X_a X_b X_c)) (tptp.combc X_a X_b X_c))))
% 10.23/10.45 (assume a2 (forall ((X_a $$unsorted)) (= (tptp.ti (tptp.fun X_a X_a) (tptp.combi X_a)) (tptp.combi X_a))))
% 10.23/10.45 (assume a3 (forall ((X_a $$unsorted) (X_b $$unsorted)) (= (tptp.ti (tptp.fun X_a (tptp.fun X_b X_a)) (tptp.combk X_a X_b)) (tptp.combk X_a X_b))))
% 10.23/10.45 (assume a4 (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) (tptp.combs X_a X_b X_c)) (tptp.combs X_a X_b X_c))))
% 10.23/10.45 (assume a5 (= (tptp.ti (tptp.fun tptp.pname (tptp.option tptp.com)) tptp.body) tptp.body))
% 10.23/10.45 (assume a6 (forall ((X_c $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_c tptp.bool) tptp.nat) (tptp.finite_card X_c)) (tptp.finite_card X_c))))
% 10.23/10.45 (assume a7 (forall ((X_b $$unsorted) (X_c $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_c)) tptp.bool) (tptp.finite_comp_fun_idem X_b X_c)) (tptp.finite_comp_fun_idem X_b X_c))))
% 10.23/10.45 (assume a8 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.finite_finite X_b)) (tptp.finite_finite X_b))))
% 10.23/10.45 (assume a9 (forall ((X_b $$unsorted) (X_c $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)))) (tptp.finite1357897459simple X_b X_c)) (tptp.finite1357897459simple X_b X_c))))
% 10.23/10.45 (assume a10 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) (tptp.finite_folding_one X_b)) (tptp.finite_folding_one X_b))))
% 10.23/10.45 (assume a11 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool)) (tptp.finite2073411215e_idem X_b)) (tptp.finite2073411215e_idem X_b))))
% 10.23/10.45 (assume a12 (forall ((X_c $$unsorted)) (=> (tptp.minus X_c) (= (tptp.ti (tptp.fun X_c (tptp.fun X_c X_c)) (tptp.minus_minus X_c)) (tptp.minus_minus X_c)))))
% 10.23/10.45 (assume a13 (forall ((X_b $$unsorted)) (=> (tptp.one X_b) (= (tptp.ti X_b (tptp.one_one X_b)) (tptp.one_one X_b)))))
% 10.23/10.45 (assume a14 (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.plus_plus X_a)) (tptp.plus_plus X_a)))))
% 10.23/10.45 (assume a15 (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.plus_plus X_a)) (tptp.plus_plus X_a)))))
% 10.23/10.45 (assume a16 (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.plus_plus X_a)) (tptp.plus_plus X_a)))))
% 10.23/10.45 (assume a17 (forall ((X_b $$unsorted)) (=> (tptp.zero X_b) (= (tptp.ti X_b (tptp.zero_zero X_b)) (tptp.zero_zero X_b)))))
% 10.23/10.45 (assume a18 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) X_b) (tptp.the X_b)) (tptp.the X_b))))
% 10.23/10.45 (assume a19 (forall ((X_a $$unsorted)) (= (tptp.ti X_a (tptp.undefined X_a)) (tptp.undefined X_a))))
% 10.23/10.45 (assume a20 (= (tptp.ti (tptp.fun tptp.nat tptp.nat) tptp.suc) tptp.suc))
% 10.23/10.45 (assume a21 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun tptp.nat X_b) (tptp.fun tptp.nat X_b))) (tptp.nat_case X_b)) (tptp.nat_case X_b))))
% 10.23/10.45 (assume a22 (= (tptp.ti (tptp.fun (tptp.option tptp.com) tptp.com) (tptp.the_1 tptp.com)) (tptp.the_1 tptp.com)))
% 10.23/10.45 (assume a23 (forall ((X_c $$unsorted)) (=> (tptp.bot X_c) (= (tptp.ti X_c (tptp.bot_bot X_c)) (tptp.bot_bot X_c)))))
% 10.23/10.45 (assume a24 (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.ord_less X_a)) (tptp.ord_less X_a)))))
% 10.23/10.45 (assume a25 (forall ((X_c $$unsorted)) (=> (tptp.ord X_c) (= (tptp.ti (tptp.fun X_c (tptp.fun X_c tptp.bool)) (tptp.ord_less_eq X_c)) (tptp.ord_less_eq X_c)))))
% 10.23/10.45 (assume a26 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) X_b)) (tptp.partial_flat_lub X_b)) (tptp.partial_flat_lub X_b))))
% 10.23/10.45 (assume a27 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.collect X_b)) (tptp.collect X_b))))
% 10.23/10.45 (assume a28 (forall ((X_b $$unsorted) (X_c $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool))) (tptp.image X_b X_c)) (tptp.image X_b X_c))))
% 10.23/10.45 (assume a29 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool))) (tptp.insert X_b)) (tptp.insert X_b))))
% 10.23/10.45 (assume a30 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) X_b) (tptp.the_elem X_b)) (tptp.the_elem X_b))))
% 10.23/10.45 (assume a31 (forall ((X_b $$unsorted) (X_c $$unsorted)) (= (tptp.ti (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool))) (tptp.sum_Plus X_b X_c)) (tptp.sum_Plus X_b X_c))))
% 10.23/10.45 (assume a32 (= (tptp.ti tptp.bool tptp.fFalse) tptp.fFalse))
% 10.23/10.45 (assume a33 (= (tptp.ti (tptp.fun tptp.bool tptp.bool) tptp.fNot) tptp.fNot))
% 10.23/10.45 (assume a34 (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue))
% 10.23/10.45 (assume a35 (= (tptp.ti (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) tptp.fconj) tptp.fconj))
% 10.23/10.45 (assume a36 (= (tptp.ti (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) tptp.fdisj) tptp.fdisj))
% 10.23/10.45 (assume a37 (forall ((X_a $$unsorted)) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fequal X_a)) (tptp.fequal X_a))))
% 10.23/10.45 (assume a38 (= (tptp.ti (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) tptp.fimplies) tptp.fimplies))
% 10.23/10.45 (assume a39 (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.ti (tptp.fun X_a X_c) B_1_1) B_2_1) (tptp.hAPP X_a X_c B_1_1 B_2_1))))
% 10.23/10.45 (assume a40 (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))))
% 10.23/10.45 (assume a41 (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.ti X_c (tptp.hAPP X_a X_c B_1_1 B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))))
% 10.23/10.45 (assume a42 (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))))
% 10.23/10.45 (assume a43 (forall ((X_b $$unsorted)) (= (tptp.ti (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) (tptp.member X_b)) (tptp.member X_b))))
% 10.23/10.45 (assume a44 (= (tptp.ti (tptp.fun tptp.x_a tptp.bool) tptp.g) tptp.g))
% 10.23/10.45 (assume a45 (= (tptp.ti (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool)) tptp.p) tptp.p))
% 10.23/10.45 (assume a46 (= (tptp.ti (tptp.fun tptp.pname tptp.bool) tptp.u) tptp.u))
% 10.23/10.45 (assume a47 (= (tptp.ti (tptp.fun tptp.com tptp.x_a) tptp.mgt) tptp.mgt))
% 10.23/10.45 (assume a48 (= (tptp.ti (tptp.fun tptp.pname tptp.x_a) tptp.mgt_call) tptp.mgt_call))
% 10.23/10.45 (assume a49 (= (tptp.ti tptp.nat tptp.na) tptp.na))
% 10.23/10.45 (assume a50 (= (tptp.ti tptp.pname tptp.pn) tptp.pn))
% 10.23/10.45 (assume a51 (= (tptp.ti (tptp.fun tptp.com tptp.bool) tptp.wt) tptp.wt))
% 10.23/10.45 (assume a52 (forall ((Ts $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) Ts) G_1)) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) tptp.p G_1) Ts)))))
% 10.23/10.45 (assume a53 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) tptp.bool (tptp.finite_finite (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.collect (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) (tptp.combc (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool))) A_3)))))))
% 10.23/10.45 (assume a54 (forall ((X_c $$unsorted) (X_b $$unsorted) (H $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) F_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) H) F_2))))))
% 10.23/10.45 (assume a55 (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) A_3))))))
% 10.23/10.45 (assume a56 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.nat (tptp.finite_card X_c) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3))))))
% 10.23/10.45 (assume a57 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) B_2)))))))
% 10.23/10.45 (assume a58 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) B_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3))) (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.ti (tptp.fun X_b tptp.bool) B_2)))))))
% 10.23/10.45 (assume a59 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)))))))
% 10.23/10.45 (assume a60 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3))))))))
% 10.23/10.45 (assume a61 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)))))))
% 10.23/10.45 (assume a62 (forall ((X_b $$unsorted) (Q_1 $$unsorted) (Pa $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) Pa))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) Q_1)))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fconj) Pa)) Q_1)))))))
% 10.23/10.45 (assume a63 (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N))))))
% 10.23/10.45 (assume a64 (forall ((K_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.collect tptp.nat) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) K_2))))))
% 10.23/10.45 (assume a65 (forall ((Na $$unsorted)) (= (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.collect tptp.nat) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) Na))) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))))
% 10.23/10.45 (assume a66 (forall ((X_b $$unsorted)) (=> (tptp.finite_finite_1 X_b) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3))))))
% 10.23/10.45 (assume a67 (forall ((X_b $$unsorted)) (=> (tptp.finite_finite_1 X_b) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3))))))
% 10.23/10.45 (assume a68 (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat tptp.suc X) (tptp.hAPP tptp.nat tptp.nat tptp.suc Y)) (= X Y))))
% 10.23/10.45 (assume a69 (forall ((Nat_2 $$unsorted) (Nat_3 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_3)) (= Nat_2 Nat_3))))
% 10.23/10.45 (assume a70 (forall ((N $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) N))))
% 10.23/10.45 (assume a71 (forall ((N $$unsorted)) (not (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))
% 10.23/10.45 (assume a72 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= M N)))))
% 10.23/10.45 (assume a73 (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J_2) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) K))))))
% 10.23/10.45 (assume a74 (forall ((M $$unsorted) (N $$unsorted)) (=> (= M N) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)))))
% 10.23/10.45 (assume a75 (forall ((M $$unsorted) (N $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)))))
% 10.23/10.45 (assume a76 (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) N))))
% 10.23/10.45 (assume a77 (forall ((I $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) I) J_2)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) I) K)) J_2))))
% 10.23/10.45 (assume a78 (forall ((X_b $$unsorted) (Pa $$unsorted) (Q_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fdisj) Pa)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) Pa))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) Q_1)))))))
% 10.23/10.45 (assume a79 (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)))))
% 10.23/10.45 (assume a80 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3))))))
% 10.23/10.45 (assume a81 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3))))))
% 10.23/10.45 (assume a82 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)))))
% 10.23/10.45 (assume a83 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N))) (= M (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))
% 10.23/10.45 (assume a84 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))
% 10.23/10.45 (assume a85 (forall ((Na $$unsorted) (M_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Na) M_1)))))
% 10.23/10.45 (assume a86 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)) (= M_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))))))
% 10.23/10.45 (assume a87 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) M_1)))))
% 10.23/10.45 (assume a88 (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) N)))))
% 10.23/10.45 (assume a89 (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) K))))
% 10.23/10.45 (assume a90 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N))))
% 10.23/10.45 (assume a91 (forall ((Na $$unsorted) (K_2 $$unsorted) (M_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) M_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) K_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) Na) K_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)))))))
% 10.23/10.45 (assume a92 (forall ((N $$unsorted) (K $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N))))))
% 10.23/10.45 (assume a93 (forall ((Na $$unsorted) (K_2 $$unsorted) (M_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) M_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) Na)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) K_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) Na) K_2)) (= M_1 Na))))))
% 10.23/10.45 (assume a94 (forall ((I $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) I)) I))))
% 10.23/10.45 (assume a95 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) L)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) L))))))
% 10.23/10.45 (assume a96 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L) M))))))
% 10.23/10.45 (assume a97 (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) M))))
% 10.23/10.45 (assume a98 (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_c tptp.bool)) B_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) B_2))))))
% 10.23/10.45 (assume a99 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) A_3))) (exists ((C_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_c tptp.bool)) C_3) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) C_3)) (= (tptp.ti (tptp.fun X_b tptp.bool) B_2) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) C_3))))))))
% 10.23/10.45 (assume a100 (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP tptp.nat X_b F N_2)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Na) N_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP tptp.nat X_b F Na)) (tptp.hAPP tptp.nat X_b F N_3)))))))))
% 10.23/10.45 (assume a101 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_2) A_3)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fconj) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combc X_b (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b)) A_3))) (tptp.hAPP X_c (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_c tptp.bool)) (tptp.fun X_c (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun X_b (tptp.fun X_c tptp.bool)) (tptp.hAPP (tptp.fun X_c (tptp.fun X_c tptp.bool)) (tptp.fun (tptp.fun X_b X_c) (tptp.fun X_b (tptp.fun X_c tptp.bool))) (tptp.combb X_c (tptp.fun X_c tptp.bool) X_b) (tptp.fequal X_c)) F)) (tptp.hAPP X_b X_c F X_2)))))))))))))
% 10.23/10.45 (assume a102 (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (=> (= (tptp.ti X_b B) (tptp.hAPP X_c X_b F X_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) B) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) A_3)))))))
% 10.23/10.45 (assume a103 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) A_3)) (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.ti (tptp.fun X_b tptp.bool) B_2))))))
% 10.23/10.45 (assume a104 (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) B_2))))))
% 10.23/10.45 (assume a105 (forall ((X_b $$unsorted) (B $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (=> (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) B_2))) (= (tptp.ti X_b A_2) (tptp.ti X_b B))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) B_2))))))
% 10.23/10.45 (assume a106 (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) A_3))) (=> (not (= (tptp.ti X_b A_2) (tptp.ti X_b B))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) A_3))))))
% 10.23/10.45 (assume a107 (forall ((I_1 $$unsorted) (Pa $$unsorted) (K_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa K_2)) (=> (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa N_2)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) K_2) I_1)))))))
% 10.23/10.45 (assume a108 (forall ((N $$unsorted) (M_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) M_3)) (exists ((M_2 $$unsorted)) (= M_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))))
% 10.23/10.45 (assume a109 (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) B_2)))))
% 10.23/10.45 (assume a110 (forall ((X_b $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) B_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fdisj) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combc X_b (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b)) B_2))))))
% 10.23/10.45 (assume a111 (forall ((X_b $$unsorted) (A_2 $$unsorted) (Pa $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) Pa)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fimplies) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2)))) Pa)))))
% 10.23/10.45 (assume a112 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3))))
% 10.23/10.45 (assume a113 (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (A_3 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) Y_1) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) Y_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)))))
% 10.23/10.45 (assume a114 (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) A_3))) (or (= (tptp.ti X_b A_2) (tptp.ti X_b B)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) A_3))))))
% 10.23/10.45 (assume a115 (forall ((X_b $$unsorted) (Y_1 $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) Y_1) A_3) X_1)) (or (= (tptp.ti X_b Y_1) (tptp.ti X_b X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_3 X_1))))))
% 10.23/10.45 (assume a116 (forall ((X_b $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2))) (= (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) B_2)) (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.ti (tptp.fun X_b tptp.bool) B_2)))))))
% 10.23/10.45 (assume a117 (forall ((X_b $$unsorted) (B $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) B_2))))))
% 10.23/10.45 (assume a118 (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) A_3) (tptp.ti (tptp.fun X_b tptp.bool) A_3)))))
% 10.23/10.45 (assume a119 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) A_3))))
% 10.23/10.45 (assume a120 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.ti (tptp.fun X_b tptp.bool) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) A_3))))))
% 10.23/10.45 (assume a121 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.ti (tptp.fun X_b tptp.bool) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))
% 10.23/10.45 (assume a122 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.ti (tptp.fun X_b tptp.bool) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) A_3)))))
% 10.23/10.45 (assume a123 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2))))))
% 10.23/10.45 (assume a124 (forall ((X_b $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2))))))
% 10.23/10.45 (assume a125 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2))))))
% 10.23/10.45 (assume a126 (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_b X_c F X_2) (tptp.hAPP X_b X_c G X_2))) (= (tptp.ti (tptp.fun X_b X_c) F) (tptp.ti (tptp.fun X_b X_c) G)))))
% 10.23/10.45 (assume a127 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool A_3 X_1)))))
% 10.23/10.45 (assume a128 (forall ((X_b $$unsorted) (Pa $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) Pa) (tptp.ti (tptp.fun X_b tptp.bool) Pa))))
% 10.23/10.45 (assume a129 (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) C_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) C_2))))))
% 10.23/10.45 (assume a130 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.ti (tptp.fun X_b tptp.bool) B_2)) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) A_3))))))))
% 10.23/10.45 (assume a131 (forall ((X_b $$unsorted) (X_c $$unsorted) (Z_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) Z_1) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) A_3))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) X_2) A_3)) (= (tptp.ti X_b Z_1) (tptp.hAPP X_c X_b F X_2)))))))
% 10.23/10.45 (assume a132 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))))
% 10.23/10.45 (assume a133 (forall ((X_c $$unsorted) (X_b $$unsorted) (B $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (=> (= (tptp.ti X_c B) (tptp.hAPP X_b X_c F X_1)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) B) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))))
% 10.23/10.45 (assume a134 (forall ((X_b $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_2) Xa) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fdisj) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) X_2))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combc X_b (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b)) Xa))))))
% 10.23/10.45 (assume a135 (forall ((X_c $$unsorted) (X_b $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (= (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) (tptp.hAPP (tptp.fun X_d tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_d X_c) (tptp.fun (tptp.fun X_d tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_d X_c) G) A_3)) (tptp.hAPP (tptp.fun X_d tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_d X_b) (tptp.fun (tptp.fun X_d tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_d X_b) (tptp.hAPP (tptp.fun X_d X_c) (tptp.fun X_d X_b) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_d X_c) (tptp.fun X_d X_b)) (tptp.combb X_c X_b X_d) F) G)) A_3))))
% 10.23/10.45 (assume a136 (forall ((X_b $$unsorted) (Y_3 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_b X_b) (tptp.combi X_b)) Y_3) (tptp.ti (tptp.fun X_b tptp.bool) Y_3))))
% 10.23/10.45 (assume a137 (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) B_2)))))
% 10.23/10.45 (assume a138 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2))))))
% 10.23/10.45 (assume a139 (forall ((X_b $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) B_2))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2))))))
% 10.23/10.45 (assume a140 (forall ((X_b $$unsorted) (B $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) B_2))))))
% 10.23/10.45 (assume a141 (forall ((X_b $$unsorted) (A_2 $$unsorted) (C_2 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) C_2) D_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) C_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) D_2))))))
% 10.23/10.45 (assume a142 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.insert X_c) A_2) B_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) (tptp.hAPP X_c X_b F A_2)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) B_2)))))
% 10.23/10.45 (assume a143 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.insert X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))
% 10.23/10.45 (assume a144 (forall ((X_b $$unsorted) (X_c $$unsorted) (B_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) A_3))) (exists ((AA $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_c tptp.bool)) AA) A_3)) (= (tptp.ti (tptp.fun X_b tptp.bool) B_2) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) AA)))))))
% 10.23/10.45 (assume a145 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_c tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) B_2))))))
% 10.23/10.45 (assume a146 (forall ((X_b $$unsorted) (X_c $$unsorted) (B $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) B) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) A_3))) (not (forall ((X_2 $$unsorted)) (=> (= (tptp.ti X_b B) (tptp.hAPP X_c X_b F X_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) X_2) A_3)))))))))
% 10.23/10.45 (assume a147 (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_2) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_2) B_2)))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))
% 10.23/10.45 (assume a148 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_2) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_2)) B_2)))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_c tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)) B_2)))))
% 10.23/10.45 (assume a149 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) X))))))
% 10.23/10.45 (assume a150 (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N_1)) (exists ((M_2 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.hAPP tptp.nat (tptp.fun (tptp.fun tptp.nat tptp.bool) tptp.bool) (tptp.member tptp.nat) X_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X_2) M_2))))))))
% 10.23/10.45 (assume a151 (forall ((G_1 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt C_1)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) X_2) tptp.u)) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) tptp.p G_1) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call X_2)) (tptp.bot_bot (tptp.fun tptp.x_a tptp.bool))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) tptp.p G_1) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.com tptp.x_a tptp.mgt C_1)) (tptp.bot_bot (tptp.fun tptp.x_a tptp.bool)))))))))
% 10.23/10.45 (assume a152 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((F $$unsorted) (G $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b X_c) tptp.bool (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b X_c) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b X_c)) F) G)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2)))))))))
% 10.23/10.45 (assume a153 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b X_c) tptp.bool (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b X_c) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b X_c)) F) G)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP X_b X_c G X_1))))))))
% 10.23/10.45 (assume a154 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b X_c) tptp.bool (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b X_c) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b X_c)) F) G)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP X_b X_c G X_1))))))))
% 10.23/10.45 (assume a155 (forall ((X_b $$unsorted) (A_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))
% 10.23/10.45 (assume a156 (forall ((X_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))
% 10.23/10.45 (assume a157 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.bot_bot (tptp.fun X_b tptp.bool))) A_3))))
% 10.23/10.45 (assume a158 (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (=> (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) A_3))))))
% 10.23/10.45 (assume a159 (forall ((X_b $$unsorted) (Pa $$unsorted)) (= (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) Pa) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)))))))
% 10.23/10.45 (assume a160 (forall ((X_b $$unsorted) (C_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))
% 10.23/10.45 (assume a161 (forall ((X_b $$unsorted) (Pa $$unsorted)) (= (= (tptp.bot_bot (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) Pa)) (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)))))))
% 10.23/10.45 (assume a162 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_2) A_3))) (not (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))
% 10.23/10.45 (assume a163 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (forall ((X_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_2) A_3)))) (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))
% 10.23/10.45 (assume a164 (forall ((X_b $$unsorted)) (= (tptp.bot_bot (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP tptp.bool (tptp.fun X_b tptp.bool) (tptp.combk tptp.bool X_b) tptp.fFalse)))))
% 10.23/10.45 (assume a165 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.bot X_c) (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_b X_c (tptp.bot_bot (tptp.fun X_b X_c)) X_2) (tptp.bot_bot X_c))))))
% 10.23/10.45 (assume a166 (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((X_1 $$unsorted)) (= (tptp.hAPP X_c X_b (tptp.bot_bot (tptp.fun X_c X_b)) X_1) (tptp.bot_bot X_b))))))
% 10.23/10.45 (assume a167 (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) (tptp.bot_bot X_a))) (= (tptp.ti X_a A_1) (tptp.bot_bot X_a)))))))
% 10.23/10.45 (assume a168 (forall ((X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) (tptp.bot_bot X_b))) (= (tptp.ti X_b A_2) (tptp.bot_bot X_b)))))))
% 10.23/10.45 (assume a169 (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.bot_bot X_a)) A_1))))))
% 10.23/10.45 (assume a170 (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (=> (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (= (tptp.ti X_b A_2) (tptp.ti X_b B)))))
% 10.23/10.45 (assume a171 (forall ((X_b $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) B) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (= (tptp.ti X_b B) (tptp.ti X_b A_2)))))
% 10.23/10.45 (assume a172 (forall ((X_b $$unsorted) (A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (= (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) C_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) D_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (or (and (= (tptp.ti X_b A_2) (tptp.ti X_b C_1)) (= (tptp.ti X_b B) (tptp.ti X_b D_1))) (and (= (tptp.ti X_b A_2) (tptp.ti X_b D_1)) (= (tptp.ti X_b B) (tptp.ti X_b C_1)))))))
% 10.23/10.45 (assume a173 (forall ((X_b $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) B) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (= (tptp.ti X_b B) (tptp.ti X_b A_2)))))
% 10.23/10.45 (assume a174 (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (not (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))
% 10.23/10.45 (assume a175 (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (not (= (tptp.bot_bot (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) A_3)))))
% 10.23/10.45 (assume a176 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))
% 10.23/10.45 (assume a177 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (= (= (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun X_c tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_c tptp.bool))))))
% 10.23/10.45 (assume a178 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted)) (= (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) (tptp.bot_bot (tptp.fun X_c tptp.bool))) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))
% 10.23/10.45 (assume a179 (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (= (= (tptp.bot_bot (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) A_3)) (= (tptp.ti (tptp.fun X_c tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_c tptp.bool))))))
% 10.23/10.45 (assume a180 (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (and (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fconj) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2))) Pa)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fconj) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2))) Pa)) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))
% 10.23/10.45 (assume a181 (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (and (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fconj) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.fequal X_b) A_2))) Pa)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fconj) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.fequal X_b) A_2))) Pa)) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))
% 10.23/10.45 (assume a182 (forall ((X_b $$unsorted) (A_2 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))
% 10.23/10.45 (assume a183 (forall ((X_b $$unsorted) (A_2 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.fequal X_b) A_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))
% 10.23/10.45 (assume a184 (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (or (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))))
% 10.23/10.45 (assume a185 (forall ((X_c $$unsorted) (X_b $$unsorted) (C_1 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) (tptp.hAPP X_c (tptp.fun X_b X_c) (tptp.combk X_c X_b) C_1)) A_3) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.insert X_c) C_1) (tptp.bot_bot (tptp.fun X_c tptp.bool)))))))
% 10.23/10.45 (assume a186 (forall ((X_c $$unsorted) (X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted)) (and (=> (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) (tptp.hAPP X_c (tptp.fun X_b X_c) (tptp.combk X_c X_b) C_1)) A_3) (tptp.bot_bot (tptp.fun X_c tptp.bool)))) (=> (not (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) (tptp.hAPP X_c (tptp.fun X_b X_c) (tptp.combk X_c X_b) C_1)) A_3) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.insert X_c) C_1) (tptp.bot_bot (tptp.fun X_c tptp.bool))))))))
% 10.23/10.45 (assume a187 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)))))))
% 10.23/10.45 (assume a188 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Z) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Z) X))))))))
% 10.23/10.45 (assume a189 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))
% 10.23/10.45 (assume a190 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Z))))))))
% 10.23/10.45 (assume a191 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))
% 10.23/10.45 (assume a192 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) A_1)) (=> (= (tptp.ti X_a B_1) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C) A_1))))))))
% 10.23/10.45 (assume a193 (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) C))))))))
% 10.23/10.45 (assume a194 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C) A_1))))))))
% 10.23/10.45 (assume a195 (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (= A_1 B_1) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) C))))))))
% 10.23/10.45 (assume a196 (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))
% 10.23/10.45 (assume a197 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))))
% 10.23/10.45 (assume a198 (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_1) X_1))))))))
% 10.23/10.45 (assume a199 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)))))))
% 10.23/10.45 (assume a200 (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) F_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (=> (forall ((A_5 $$unsorted) (F_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) F_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_5) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_5) F_3))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa F_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_5) F_3)))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa F_2))))))))
% 10.23/10.45 (assume a201 (forall ((Pn $$unsorted) (G_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) tptp.p (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call Pn)) G_1)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.com tptp.x_a tptp.mgt (tptp.hAPP (tptp.option tptp.com) tptp.com (tptp.the_1 tptp.com) (tptp.hAPP tptp.pname (tptp.option tptp.com) tptp.body Pn)))) (tptp.bot_bot (tptp.fun tptp.x_a tptp.bool))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) tptp.p G_1) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call Pn)) (tptp.bot_bot (tptp.fun tptp.x_a tptp.bool))))))))
% 10.23/10.45 (assume a202 (forall ((X_b $$unsorted) (Pa $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (=> (forall ((X_2 $$unsorted) (F_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) F_3)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_2) F_3))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa F_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_2) F_3))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa F_2)))))))
% 10.23/10.45 (assume a203 (forall ((X_b $$unsorted) (A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_2)) (or (= (tptp.ti (tptp.fun X_b tptp.bool) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (exists ((A_4 $$unsorted) (A_5 $$unsorted)) (and (= (tptp.ti (tptp.fun X_b tptp.bool) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_5) A_4)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_4))))))))
% 10.23/10.45 (assume a204 (forall ((U $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_2) (tptp.hAPP tptp.nat tptp.nat F N_2)))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.collect tptp.nat) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat tptp.nat) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun (tptp.fun tptp.nat tptp.nat) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool))) (tptp.combb tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.nat) (tptp.ord_less_eq tptp.nat)) F)) U)))))))
% 10.23/10.45 (assume a205 (forall ((X_b $$unsorted) (X_1 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the_elem X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (tptp.ti X_b X_1))))
% 10.23/10.45 (assume a206 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (not (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (exists ((X_2 $$unsorted) (B_4 $$unsorted)) (and (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_2) B_4)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_2) B_4))))))))
% 10.23/10.45 (assume a207 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((F $$unsorted) (G $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c G X_2)))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b X_c) tptp.bool (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b X_c) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b X_c)) F) G)))))))
% 10.23/10.45 (assume a208 (forall ((Pn $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) Pn) tptp.u)) (tptp.hBOOL (tptp.hAPP tptp.com tptp.bool tptp.wt (tptp.hAPP (tptp.option tptp.com) tptp.com (tptp.the_1 tptp.com) (tptp.hAPP tptp.pname (tptp.option tptp.com) tptp.body Pn)))))))
% 10.23/10.45 (assume a209 (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) C_1) D_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) B)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) C_1) D_1))))))))
% 10.23/10.45 (assume a210 (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (= (tptp.ti (tptp.fun X_b tptp.bool) B_2) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 B_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 A_3))))))))
% 10.23/10.45 (assume a211 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_1) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 A_3))))))))
% 10.23/10.45 (assume a212 (forall ((X_b $$unsorted) (Pa $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) F_2)) (=> (not (= (tptp.ti (tptp.fun X_b tptp.bool) F_2) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_2) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))) (=> (forall ((X_2 $$unsorted) (F_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) F_3)) (=> (not (= (tptp.ti (tptp.fun X_b tptp.bool) F_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_2) F_3))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa F_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_2) F_3)))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa F_2))))))))
% 10.23/10.45 (assume a213 (forall ((X_b $$unsorted) (X_3 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the_elem X_b) X_3) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.fun (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b tptp.bool)) (tptp.combb (tptp.fun X_b tptp.bool) tptp.bool X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.fequal (tptp.fun X_b tptp.bool)) X_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool))) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun X_b tptp.bool))) (tptp.combc X_b (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b)) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))))
% 10.23/10.45 (assume a214 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (=> (not (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_1) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 A_3)))))))))
% 10.23/10.45 (assume a215 (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))))))
% 10.23/10.45 (assume a216 (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_2)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_1) X_1) (tptp.ti X_b X_1)))))
% 10.23/10.45 (assume a217 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))
% 10.23/10.45 (assume a218 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (tptp.ti (tptp.fun X_b tptp.bool) A_3))))
% 10.23/10.45 (assume a219 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.bot_bot (tptp.fun X_b tptp.bool))) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))
% 10.23/10.45 (assume a220 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3))))))
% 10.23/10.45 (assume a221 (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2)))))
% 10.23/10.45 (assume a222 (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$unsorted)) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2)))))))
% 10.23/10.45 (assume a223 (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) C_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) B_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) C_2) A_3)) (tptp.ti (tptp.fun X_b tptp.bool) A_3))))))
% 10.23/10.45 (assume a224 (forall ((X_b $$unsorted) (D_2 $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted) (C_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) C_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) D_2) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) C_2) D_2)))))))
% 10.23/10.45 (assume a225 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2)) A_3))))
% 10.23/10.45 (assume a226 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (and (=> (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 A_3) (tptp.ti X_b X_1))) (=> (not (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_1) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))))))))))
% 10.23/10.45 (assume a227 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (and (=> (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.ti X_b X_1))) (=> (not (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_1) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))))))))
% 10.23/10.45 (assume a228 (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) B_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))
% 10.23/10.45 (assume a229 (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) B_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) B_2))))
% 10.23/10.45 (assume a230 (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) A_3))))
% 10.23/10.45 (assume a231 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (tptp.ti (tptp.fun X_b tptp.bool) A_3)))))
% 10.23/10.45 (assume a232 (forall ((X_b $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (tptp.ti (tptp.fun X_b tptp.bool) A_3)))))
% 10.23/10.45 (assume a233 (forall ((X_b $$unsorted) (A_3 $$unsorted) (A_2 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) B_2)))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))))))
% 10.23/10.45 (assume a234 (forall ((X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) A_3)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) B_2))) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_c X_b) F) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.minus_minus (tptp.fun X_c tptp.bool)) A_3) B_2))))))
% 10.23/10.45 (assume a235 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_1) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 A_3)))))))
% 10.23/10.45 (assume a236 (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) B_2)))))))
% 10.23/10.45 (assume a237 (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) B_2))) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) B_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))))
% 10.23/10.45 (assume a238 (forall ((X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) C_1) D_1)) (= (= (tptp.ti X_b A_2) (tptp.ti X_b B)) (= (tptp.ti X_b C_1) (tptp.ti X_b D_1))))))))
% 10.23/10.45 (assume a239 (forall ((X_b $$unsorted) (X_1 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (tptp.ti X_b X_1)))))
% 10.23/10.45 (assume a240 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) B_2)))))))
% 10.23/10.45 (assume a241 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) B_2))) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2)))))))
% 10.23/10.45 (assume a242 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3))))))
% 10.23/10.45 (assume a243 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))))))
% 10.23/10.45 (assume a244 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3))))))
% 10.23/10.45 (assume a245 (forall ((X_b $$unsorted) (N_1 $$unsorted) (H $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite2073411215e_idem X_b) F) F_2)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (= (tptp.hAPP X_b X_b H (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_2) Y_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F (tptp.hAPP X_b X_b H X_2)) (tptp.hAPP X_b X_b H Y_2)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) N_1)) (=> (not (= (tptp.ti (tptp.fun X_b tptp.bool) N_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (= (tptp.hAPP X_b X_b H (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 N_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image X_b X_b) H) N_1)))))))))
% 10.23/10.45 (assume a246 (forall ((X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun (tptp.fun (tptp.fun X_b tptp.bool) X_b) tptp.bool) (tptp.finite_folding_one X_b) F) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F X_2) Y_2)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) Y_2) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b F_2 A_3)) A_3))))))))
% 10.23/10.45 (assume a247 (forall ((X_b $$unsorted) (Pa $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa A_3)) (=> (forall ((A_5 $$unsorted) (A_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_4)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_5) A_4)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa A_4)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_4) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_5) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool Pa (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))))
% 10.23/10.45 (assume a248 (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool))) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) X_1) A_3)) (= (tptp.hAPP (tptp.fun X_c tptp.bool) X_b F_2 A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP (tptp.fun X_c tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.minus_minus (tptp.fun X_c tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.insert X_c) X_1) (tptp.bot_bot (tptp.fun X_c tptp.bool))))))))))))
% 10.23/10.45 (assume a249 (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool))) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) A_3)) (= (tptp.hAPP (tptp.fun X_c tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.insert X_c) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP (tptp.fun X_c tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.minus_minus (tptp.fun X_c tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.insert X_c) X_1) (tptp.bot_bot (tptp.fun X_c tptp.bool)))))))))))
% 10.23/10.45 (assume a250 (forall ((X_b $$unsorted) (X_1 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.fequal X_b) X_1)) (tptp.ti X_b X_1))))
% 10.23/10.45 (assume a251 (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) B_2)))))))
% 10.23/10.45 (assume a252 (forall ((X_b $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) B_2))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2)))))))
% 10.23/10.45 (assume a253 (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) B_2))))))
% 10.23/10.45 (assume a254 (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) A_3)))))
% 10.23/10.45 (assume a255 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2)) B_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))))
% 10.23/10.45 (assume a256 (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) A_3)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) B_2)))))))
% 10.23/10.45 (assume a257 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.collect X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fconj) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combc X_b (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b)) A_3))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combb tptp.bool tptp.bool X_b) tptp.fNot) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combc X_b (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b)) B_2)))))))
% 10.23/10.45 (assume a258 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool))) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_2)) (= (tptp.hAPP (tptp.fun X_c tptp.bool) X_b F_2 (tptp.bot_bot (tptp.fun X_c tptp.bool))) (tptp.ti X_b Z_1)))))
% 10.23/10.45 (assume a259 (forall ((X_c $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool))) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) X_1) A_3))) (= (tptp.hAPP (tptp.fun X_c tptp.bool) X_b F_2 (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.insert X_c) X_1) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) F (tptp.hAPP X_c X_b G X_1)) (tptp.hAPP (tptp.fun X_c tptp.bool) X_b F_2 A_3))))))))
% 10.23/10.45 (assume a260 (forall ((X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (Pa $$unsorted)) (and (=> (tptp.hBOOL Pa) (= (tptp.ti X_b X_1) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fconj) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combb tptp.bool tptp.bool X_b) (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies Pa)) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) X_1)))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combb tptp.bool tptp.bool X_b) (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies (tptp.hAPP tptp.bool tptp.bool tptp.fNot Pa))) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) Y_1)))))) (=> (not (tptp.hBOOL Pa)) (= (tptp.ti X_b Y_1) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) X_b) tptp.fconj) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combb tptp.bool tptp.bool X_b) (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies Pa)) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) X_1)))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combb tptp.bool tptp.bool X_b) (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies (tptp.hAPP tptp.bool tptp.bool tptp.fNot Pa))) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) Y_1)))))))))
% 10.23/10.45 (assume a261 (forall ((X_b $$unsorted) (A_2 $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.combc X_b X_b tptp.bool) (tptp.fequal X_b)) A_2)) (tptp.ti X_b A_2))))
% 10.23/10.45 (assume a262 (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_2)))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_2))))))
% 10.23/10.45 (assume a263 (forall ((X_c $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Z_1 $$unsorted) (G $$unsorted) (F_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool)) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b X_b)) (tptp.fun X_b (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.fun (tptp.fun X_c tptp.bool) X_b) tptp.bool))) (tptp.finite1357897459simple X_b X_c) F) Z_1) G) F_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) A_3)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) X_2) A_3)) (= (tptp.hAPP X_c X_b G X_2) (tptp.ti X_b Z_1)))) (= (tptp.hAPP (tptp.fun X_c tptp.bool) X_b F_2 A_3) (tptp.ti X_b Z_1)))))))
% 10.23/10.45 (assume a264 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.minus X_c) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X_2 $$unsorted)) (= (tptp.hAPP X_b X_c (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun X_b X_c) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b X_c) (tptp.fun X_b X_c)) (tptp.minus_minus (tptp.fun X_b X_c)) A_3) B_2) X_2) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.minus_minus X_c) (tptp.hAPP X_b X_c A_3 X_2)) (tptp.hAPP X_b X_c B_2 X_2)))))))
% 10.23/10.45 (assume a265 (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (tptp.minus X_b) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted)) (= (tptp.hAPP X_c X_b (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun X_c X_b) (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun (tptp.fun X_c X_b) (tptp.fun X_c X_b)) (tptp.minus_minus (tptp.fun X_c X_b)) A_3) B_2) X_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP X_c X_b A_3 X_1)) (tptp.hAPP X_c X_b B_2 X_1)))))))
% 10.23/10.45 (assume a266 (forall ((X_b $$unsorted) (Pa $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (= (tptp.ti X_b X_2) (tptp.ti X_b A_2)))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa)))))))
% 10.23/10.45 (assume a267 (forall ((X_b $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_2)) (= (tptp.ti X_b Y_2) (tptp.ti X_b X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa))))))
% 10.23/10.45 (assume a268 (forall ((X_b $$unsorted) (A_2 $$unsorted) (Pa $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa X_2)) (forall ((Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa Y_2)) (= (tptp.ti X_b Y_2) (tptp.ti X_b X_2)))))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Pa A_2)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) Pa) (tptp.ti X_b A_2))))))
% 10.23/10.45 (assume a269 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B $$unsorted)) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) X_b) (tptp.partial_flat_lub X_b) B) A_3) (tptp.ti X_b B))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) X_b) (tptp.partial_flat_lub X_b) B) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) X_b (tptp.the X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool)) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.combc X_b (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) B) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))))))
% 10.23/10.45 (assume a270 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.one_one tptp.nat)))))))
% 10.23/10.45 (assume a271 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.one_one tptp.nat)))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)))))))
% 10.23/10.45 (assume a272 (forall ((X_b $$unsorted)) (=> (tptp.one X_b) (forall ((X_1 $$unsorted)) (= (= (tptp.one_one X_b) (tptp.ti X_b X_1)) (= (tptp.ti X_b X_1) (tptp.one_one X_b)))))))
% 10.23/10.45 (assume a273 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) (tptp.one_one tptp.nat))) N))))
% 10.23/10.45 (assume a274 (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.one_one tptp.nat)) N)))
% 10.23/10.45 (assume a275 (forall ((X_b $$unsorted) (B_2 $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) A_2) B_2))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) A_2) B_2))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) B_2))) (tptp.one_one tptp.nat))))))))
% 10.23/10.45 (assume a276 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))))))
% 10.23/10.45 (assume a277 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))))))
% 10.23/10.45 (assume a278 (forall ((X_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool))) tptp.bool (tptp.finite_comp_fun_idem X_b (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool))) (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool))) (tptp.fun (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)))) (tptp.combb (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) X_b) (tptp.hAPP (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool))) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool))) (tptp.combc (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool))) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b (tptp.fun X_b tptp.bool))) (tptp.combc X_b (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b)) (tptp.bot_bot (tptp.fun X_b tptp.bool))))))))
% 10.23/10.45 (assume a279 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.hAPP tptp.bool (tptp.fun (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool)) (tptp.nat_case tptp.bool) tptp.fFalse) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1)) Na)))))
% 10.23/10.45 (assume a280 (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) B) C_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) B)))))))
% 10.23/10.45 (assume a281 (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) C_1) A_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) C_1) B))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) B)))))))
% 10.23/10.45 (assume a282 (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) C))))))))
% 10.23/10.45 (assume a283 (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C) B_1))))))))
% 10.23/10.45 (assume a284 (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) D)))))))))
% 10.23/10.45 (assume a285 (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) B_1)))))))
% 10.23/10.45 (assume a286 (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C) B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) B_1)))))))
% 10.23/10.45 (assume a287 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)))))
% 10.23/10.45 (assume a288 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)))))
% 10.23/10.45 (assume a289 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))
% 10.23/10.45 (assume a290 (forall ((X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (Z_1 $$unsorted) (F $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_c)) tptp.bool (tptp.finite_comp_fun_idem X_b X_c) F)) (= (tptp.hAPP X_c X_c (tptp.hAPP X_b (tptp.fun X_c X_c) F X_1) (tptp.hAPP X_c X_c (tptp.hAPP X_b (tptp.fun X_c X_c) F X_1) Z_1)) (tptp.hAPP X_c X_c (tptp.hAPP X_b (tptp.fun X_c X_c) F X_1) Z_1)))))
% 10.23/10.45 (assume a291 (forall ((M_1 $$unsorted) (K_2 $$unsorted) (Na $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) K_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Na) K_2)) (= M_1 Na))))
% 10.23/10.45 (assume a292 (forall ((K_2 $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2) M_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2) Na)) (= M_1 Na))))
% 10.23/10.45 (assume a293 (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) K)))))
% 10.23/10.45 (assume a294 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) X) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) X) Z)))))
% 10.23/10.45 (assume a295 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M))))
% 10.23/10.45 (assume a296 (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C) A_1)) (= (tptp.ti X_a B_1) (tptp.ti X_a C)))))))
% 10.23/10.45 (assume a297 (forall ((X_a $$unsorted)) (=> (tptp.cancel146912293up_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (= (tptp.ti X_a B_1) (tptp.ti X_a C)))))))
% 10.23/10.45 (assume a298 (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (= (tptp.ti X_a B_1) (tptp.ti X_a C)))))))
% 10.23/10.45 (assume a299 (forall ((X_b $$unsorted)) (=> (tptp.cancel_semigroup_add X_b) (forall ((B $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) B) A_2) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) C_1) A_2)) (= (tptp.ti X_b B) (tptp.ti X_b C_1)))))))
% 10.23/10.45 (assume a300 (forall ((X_b $$unsorted)) (=> (tptp.cancel_semigroup_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) B) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) C_1)) (= (tptp.ti X_b B) (tptp.ti X_b C_1)))))))
% 10.23/10.45 (assume a301 (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted) (C $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B_1)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) C)))))))
% 10.23/10.45 (assume a302 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)) N) M)))
% 10.23/10.45 (assume a303 (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)) N) M)))
% 10.23/10.45 (assume a304 (forall ((I $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) I) J_2)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) K)))))
% 10.23/10.45 (assume a305 (forall ((K $$unsorted) (M $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N))))
% 10.23/10.45 (assume a306 (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N))))
% 10.23/10.45 (assume a307 (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)))))
% 10.23/10.45 (assume a308 (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)))))
% 10.23/10.45 (assume a309 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)) (exists ((K_1 $$unsorted)) (= Na (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) K_1))))))
% 10.23/10.45 (assume a310 (forall ((K_2 $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2) M_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)))))
% 10.23/10.45 (assume a311 (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) M))))))
% 10.23/10.45 (assume a312 (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) J_2))))))
% 10.23/10.45 (assume a313 (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) K))))))
% 10.23/10.45 (assume a314 (forall ((K $$unsorted) (L $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) L)))))))
% 10.23/10.45 (assume a315 (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) N)))))
% 10.23/10.45 (assume a316 (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)))))
% 10.23/10.45 (assume a317 (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) N)) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) N))))))))
% 10.23/10.45 (assume a318 (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) B_1)) B_1) (tptp.ti X_a A_1))))))
% 10.23/10.45 (assume a319 (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B_1)) B_1) (tptp.ti X_a A_1))))))
% 10.23/10.45 (assume a320 (forall ((X_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool))) tptp.bool (tptp.finite_comp_fun_idem X_b (tptp.fun X_b tptp.bool)) (tptp.insert X_b)))))
% 10.23/10.45 (assume a321 (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) I)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) K)) I)))))
% 10.23/10.45 (assume a322 (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) K)) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) I)) K)))))
% 10.23/10.45 (assume a323 (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) J_2)) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) K))))))
% 10.23/10.45 (assume a324 (forall ((K_2 $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_1)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_1) I_1) K_2) (= J_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2) I_1))))))
% 10.23/10.45 (assume a325 (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) N) M))))
% 10.23/10.45 (assume a326 (forall ((I_1 $$unsorted) (K_2 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) J_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_1) K_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_1) K_2)) J_1))))))
% 10.23/10.45 (assume a327 (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) J_2)) K)))))
% 10.23/10.45 (assume a328 (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) M))))
% 10.23/10.45 (assume a329 (forall ((M $$unsorted) (K $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)) K))))))
% 10.23/10.45 (assume a330 (forall ((J_1 $$unsorted) (K_2 $$unsorted) (I_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_1) K_2)) I_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_1) K_2))))))
% 10.23/10.45 (assume a331 (forall ((I $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) K)) J_2)))))
% 10.23/10.45 (assume a332 (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat)))))
% 10.23/10.45 (assume a333 (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) N))))
% 10.23/10.45 (assume a334 (forall ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Nat_2 $$unsorted)) (= (tptp.hAPP tptp.nat X_b (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun tptp.nat X_b) (tptp.hAPP X_b (tptp.fun (tptp.fun tptp.nat X_b) (tptp.fun tptp.nat X_b)) (tptp.nat_case X_b) F1) F2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_2)) (tptp.hAPP tptp.nat X_b F2 Nat_2))))
% 10.23/10.45 (assume a335 (forall ((M $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) K))) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc J_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K) M))))))
% 10.23/10.45 (assume a336 (forall ((M $$unsorted) (K $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) K))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K)) (tptp.hAPP tptp.nat tptp.nat tptp.suc J_2))))))
% 10.23/10.45 (assume a337 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)))))))
% 10.23/10.45 (assume a338 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z))))))
% 10.23/10.45 (assume a339 (forall ((Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X) Z)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z))))))
% 10.23/10.45 (assume a340 (forall ((X_b $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) Y_1) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) Y_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3))))))))
% 10.23/10.45 (assume a341 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)))))))
% 10.23/10.45 (assume a342 (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))
% 10.23/10.45 (assume a343 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))
% 10.23/10.45 (assume a344 (forall ((K_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.collect tptp.nat) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) K_2))))))
% 10.23/10.45 (assume a345 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z))))))
% 10.23/10.45 (assume a346 (forall ((Y $$unsorted) (X $$unsorted) (Z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X) Z)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z))))))
% 10.23/10.45 (assume a347 (forall ((I $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) J_2)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) K)))))
% 10.23/10.45 (assume a348 (forall ((M $$unsorted) (N $$unsorted) (K $$unsorted) (L $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) K) L)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) L) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))))))
% 10.23/10.45 (assume a349 (forall ((K $$unsorted) (L $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) K) L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) L)))))))
% 10.23/10.45 (assume a350 (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) K))))))
% 10.23/10.45 (assume a351 (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) J_2))))))
% 10.23/10.45 (assume a352 (forall ((M $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) M))))))
% 10.23/10.45 (assume a353 (forall ((K_2 $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2) M_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_2) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)))))
% 10.23/10.45 (assume a354 (forall ((J_2 $$unsorted) (I $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) I)) I)))))
% 10.23/10.45 (assume a355 (forall ((I $$unsorted) (J_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) J_2)) I)))))
% 10.23/10.45 (assume a356 (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C) B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1)))))))
% 10.23/10.45 (assume a357 (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1)))))))
% 10.23/10.45 (assume a358 (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) D)))))))))
% 10.23/10.45 (assume a359 (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C) B_1))))))))
% 10.23/10.45 (assume a360 (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) C))))))))
% 10.23/10.45 (assume a361 (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) C_1) A_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) C_1) B))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) B)))))))
% 10.23/10.45 (assume a362 (forall ((X_b $$unsorted)) (=> (tptp.ordere236663937imp_le X_b) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) C_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) B) C_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) B)))))))
% 10.23/10.45 (assume a363 (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (=> (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) C_1) D_1)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) B)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) C_1) D_1))))))))
% 10.23/10.45 (assume a364 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)))))
% 10.23/10.45 (assume a365 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)))))
% 10.23/10.45 (assume a366 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))) (= M N)))))
% 10.23/10.45 (assume a367 (forall ((K $$unsorted) (I $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_2) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc I)) K))))))
% 10.23/10.45 (assume a368 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (=> (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N))))))
% 10.23/10.45 (assume a369 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))
% 10.23/10.45 (assume a370 (forall ((N $$unsorted) (M $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (= M N)))))
% 10.23/10.45 (assume a371 (forall ((Na $$unsorted) (M_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) M_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))) (= Na M_1)))))
% 10.23/10.45 (assume a372 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)))))
% 10.23/10.45 (assume a373 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)) (= M_1 Na)))))
% 10.23/10.45 (assume a374 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))))))
% 10.23/10.45 (assume a375 (forall ((M $$unsorted) (N $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)))))
% 10.23/10.45 (assume a376 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (=> (not (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))))))
% 10.23/10.45 (assume a377 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)))))
% 10.23/10.45 (assume a378 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)) (= M_1 Na)))))
% 10.23/10.45 (assume a379 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)) (not (= M_1 Na))))))
% 10.23/10.45 (assume a380 (forall ((L $$unsorted) (M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) L)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L) M)))))))
% 10.23/10.45 (assume a381 (forall ((N $$unsorted) (J_2 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_2) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) N)) K)))))
% 10.23/10.45 (assume a382 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) X)))))))
% 10.23/10.45 (assume a383 (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (not (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_1) X_1))))))))
% 10.23/10.45 (assume a384 (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1))) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_1) X_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))
% 10.23/10.45 (assume a385 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X)))))))
% 10.23/10.45 (assume a386 (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_1) X_1))) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1))) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))
% 10.23/10.45 (assume a387 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X))))))))
% 10.23/10.45 (assume a388 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))
% 10.23/10.45 (assume a389 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X))))))))
% 10.23/10.45 (assume a390 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X))))))))
% 10.23/10.45 (assume a391 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))
% 10.23/10.45 (assume a392 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a Y) (tptp.ti X_a X))))))))
% 10.23/10.45 (assume a393 (forall ((X_b $$unsorted)) (=> (tptp.preorder X_b) (forall ((Pa $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_1) X_1)) (tptp.hBOOL Pa)))))))
% 10.23/10.45 (assume a394 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) B_1) A_1))))))))
% 10.23/10.45 (assume a395 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) B_1) A_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1))))))))
% 10.23/10.45 (assume a396 (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (= A_1 B_1) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) C))))))))
% 10.23/10.45 (assume a397 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C) A_1))))))))
% 10.23/10.45 (assume a398 (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1)) (=> (= B_1 C) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) C))))))))
% 10.23/10.45 (assume a399 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) B_1) A_1)) (=> (= (tptp.ti X_a B_1) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C) A_1))))))))
% 10.23/10.45 (assume a400 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Z))))))))
% 10.23/10.45 (assume a401 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Z) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Z) X))))))))
% 10.23/10.45 (assume a402 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X))))))))
% 10.23/10.45 (assume a403 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X))))))))
% 10.23/10.45 (assume a404 (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X) Y)))))
% 10.23/10.45 (assume a405 (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N)))))
% 10.23/10.45 (assume a406 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (not (= M_1 Na)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) M_1))))))
% 10.23/10.45 (assume a407 (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X) Y))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Y) X))))))
% 10.23/10.45 (assume a408 (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N)))))
% 10.23/10.45 (assume a409 (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) M)) (not (= M N)))))
% 10.23/10.45 (assume a410 (forall ((S $$unsorted) (T_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) S) T_3)) (not (= S T_3)))))
% 10.23/10.45 (assume a411 (forall ((Pa $$unsorted) (M_1 $$unsorted) (Na $$unsorted)) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) Pa Na) M_1))) (=> (=> (= M_1 Na) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) Pa Na) M_1))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) M_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) Pa Na) M_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) Pa Na) M_1)))))))
% 10.23/10.45 (assume a412 (forall ((X_a $$unsorted)) (=> (tptp.bot X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.bot_bot X_a))))))))
% 10.23/10.45 (assume a413 (forall ((X_b $$unsorted)) (=> (tptp.bot X_b) (forall ((A_2 $$unsorted)) (= (not (= (tptp.ti X_b A_2) (tptp.bot_bot X_b))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.bot_bot X_b)) A_2)))))))
% 10.23/10.45 (assume a414 (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_1) X_1)))))))
% 10.23/10.45 (assume a415 (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_1) X_1)))))))
% 10.23/10.45 (assume a416 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X)))))))
% 10.23/10.45 (assume a417 (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1)) (not (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1)))))))))
% 10.23/10.45 (assume a418 (forall ((X_b $$unsorted)) (=> (tptp.preorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_1) X_1)))))))))
% 10.23/10.45 (assume a419 (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1)) (or (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))
% 10.23/10.45 (assume a420 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)))))))
% 10.23/10.45 (assume a421 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)))))))
% 10.23/10.45 (assume a422 (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1)) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))
% 10.23/10.45 (assume a423 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1))))))))
% 10.23/10.45 (assume a424 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) B_1) A_1))))))))
% 10.23/10.45 (assume a425 (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y))))))))
% 10.23/10.45 (assume a426 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))))
% 10.23/10.45 (assume a427 (forall ((X_b $$unsorted)) (=> (tptp.linorder X_b) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_1) Y_1)) (= (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_1) Y_1))) (= (tptp.ti X_b X_1) (tptp.ti X_b Y_1))))))))
% 10.23/10.45 (assume a428 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))
% 10.23/10.45 (assume a429 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) B_1)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1))))))))
% 10.23/10.45 (assume a430 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) A_1)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) B_1) A_1))))))))
% 10.23/10.45 (assume a431 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Z))))))))
% 10.23/10.45 (assume a432 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Z) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Z) X))))))))
% 10.23/10.45 (assume a433 (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Z))))))))
% 10.23/10.45 (assume a434 (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z $$unsorted) (Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Z) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Z) X))))))))
% 10.23/10.45 (assume a435 (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N_1)) (exists ((M_2 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.hAPP tptp.nat (tptp.fun (tptp.fun tptp.nat tptp.bool) tptp.bool) (tptp.member tptp.nat) X_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X_2) M_2))))))))
% 10.23/10.45 (assume a436 (forall ((X_b $$unsorted) (A_3 $$unsorted) (F $$unsorted) (Na $$unsorted)) (=> (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun (tptp.fun tptp.nat tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image tptp.nat X_b) F) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.collect tptp.nat) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) Na)))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)))))
% 10.23/10.45 (assume a437 (forall ((Na $$unsorted)) (= (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.collect tptp.nat) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) Na))) Na)))
% 10.23/10.45 (assume a438 (forall ((Pa $$unsorted) (I_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.collect tptp.nat) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool)) (tptp.combs tptp.nat tptp.bool tptp.bool) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat (tptp.fun tptp.bool tptp.bool)) (tptp.hAPP (tptp.fun tptp.bool (tptp.fun tptp.bool tptp.bool)) (tptp.fun (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat (tptp.fun tptp.bool tptp.bool))) (tptp.combb tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.nat) tptp.fconj) Pa)) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) I_1)))))))
% 10.23/10.45 (assume a439 (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) D)))))))))
% 10.23/10.45 (assume a440 (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) D)))))))))
% 10.23/10.45 (assume a441 (forall ((I $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I) M))))))
% 10.23/10.45 (assume a442 (forall ((I $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) I))))))
% 10.23/10.45 (assume a443 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)) (exists ((K_1 $$unsorted)) (= Na (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) K_1)))))))
% 10.23/10.45 (assume a444 (forall ((Na $$unsorted) (M_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) M_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na)) M_1)))))
% 10.23/10.45 (assume a445 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc Na))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)))))
% 10.23/10.45 (assume a446 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1)) Na)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)))))
% 10.23/10.45 (assume a447 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))
% 10.23/10.45 (assume a448 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)))))
% 10.23/10.45 (assume a449 (forall ((M_1 $$unsorted) (Na $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc M_1))) (= Na M_1)))))
% 10.23/10.45 (assume a450 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)))))
% 10.23/10.45 (assume a451 (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))))
% 10.23/10.45 (assume a452 (forall ((M $$unsorted) (N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) M))))
% 10.23/10.45 (assume a453 (forall ((I_1 $$unsorted) (J_1 $$unsorted) (K_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_1) K_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_1) K_2)) J_1)))))
% 10.23/10.45 (assume a454 (forall ((C $$unsorted) (A_1 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) A_1) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) C) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) B_1) C)))))))
% 10.23/10.45 (assume a455 (forall ((Na $$unsorted) (K_2 $$unsorted) (M_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) M_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_2) Na)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) K_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) Na) K_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_1) Na)))))))
% 10.23/10.45 (assume a456 (forall ((X_2 $$unsorted)) (= (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X_2) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc X_2)))))
% 10.23/10.45 (assume a457 (forall ((M_1 $$unsorted) (K_2 $$unsorted) (F $$unsorted)) (=> (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat F M_2)) (tptp.hAPP tptp.nat tptp.nat F N_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat F M_1)) K_2)) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) K_2)))))))
% 10.23/10.45 (assume a458 (forall ((Pa $$unsorted) (I_1 $$unsorted) (J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa J_1)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool Pa I_1)))))))
% 10.23/10.45 (assume a459 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (exists ((K_1 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K_1)))))))
% 10.23/10.45 (assume a460 (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) B_2) C_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) C_2))))))
% 10.23/10.45 (assume a461 (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) B_2) C_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) C_2))))))
% 10.23/10.45 (assume a462 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))
% 10.23/10.45 (assume a463 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2)) (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.ti (tptp.fun X_b tptp.bool) B_2))))))
% 10.23/10.45 (assume a464 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (not (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.ti (tptp.fun X_b tptp.bool) B_2)))))))
% 10.23/10.45 (assume a465 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool)))))))
% 10.23/10.45 (assume a466 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (tptp.ord X_c) (forall ((F $$unsorted) (G $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b X_c) tptp.bool (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b X_c) tptp.bool) (tptp.ord_less (tptp.fun X_b X_c)) F) G)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b X_c) tptp.bool (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b X_c) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b X_c)) F) G)) (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b X_c) tptp.bool (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b X_c) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b X_c)) G) F)))))))))
% 10.23/10.45 (assume a467 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) B_2)))))))
% 10.23/10.45 (assume a468 (forall ((X_b $$unsorted) (A_3 $$unsorted) (X_1 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) B_2))) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2))) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) A_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) (tptp.bot_bot (tptp.fun X_b tptp.bool))))) B_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))))))
% 10.23/10.45 (assume a469 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) B_2))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2)))))))
% 10.23/10.45 (assume a470 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (exists ((N_2 $$unsorted) (F_1 $$unsorted)) (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun (tptp.fun tptp.nat tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.image tptp.nat X_b) F_1) (tptp.hAPP (tptp.fun tptp.nat tptp.bool) (tptp.fun tptp.nat tptp.bool) (tptp.collect tptp.nat) (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) N_2))))))))
% 10.23/10.45 (assume a471 (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (N_3 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F N_2)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) N_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F Na)) (tptp.hAPP tptp.nat X_b F N_3)))))))))
% 10.23/10.45 (assume a472 (forall ((X_b $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) C_1) B_2))))))
% 10.23/10.45 (assume a473 (forall ((X_b $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) B_2) C_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) C_2))))))
% 10.23/10.45 (assume a474 (forall ((X_b $$unsorted)) (=> (tptp.order X_b) (forall ((Na $$unsorted) (M_1 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F N_2)) (tptp.hAPP tptp.nat X_b F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP tptp.nat X_b F Na)) (tptp.hAPP tptp.nat X_b F M_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Na) M_1))))))))
% 10.23/10.45 (assume a475 (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.one_one X_a))))))))
% 10.23/10.45 (assume a476 (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) X))))))))
% 10.23/10.45 (assume a477 (forall ((Na $$unsorted) (N_1 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.hAPP tptp.nat (tptp.fun (tptp.fun tptp.nat tptp.bool) tptp.bool) (tptp.member tptp.nat) X_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X_2) Na)))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite tptp.nat) N_1)))))
% 10.23/10.45 (assume a478 (forall ((X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less (tptp.fun X_b tptp.bool)) A_3) B_2)) (exists ((B_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) B_3) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.minus_minus (tptp.fun X_b tptp.bool)) B_2) A_3)))))))
% 10.23/10.45 (assume a479 (forall ((I_1 $$unsorted) (J_1 $$unsorted) (F $$unsorted)) (=> (forall ((I_2 $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat F I_2)) (tptp.hAPP tptp.nat tptp.nat F J))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat F I_1)) (tptp.hAPP tptp.nat tptp.nat F J_1)))))))
% 10.23/10.45 (assume a480 (forall ((I $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc I)) K)) (not (forall ((J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J)) (not (= K (tptp.hAPP tptp.nat tptp.nat tptp.suc J)))))))))
% 10.23/10.45 (assume a481 (forall ((I $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) K)) (=> (not (= K (tptp.hAPP tptp.nat tptp.nat tptp.suc I))) (not (forall ((J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) J)) (not (= K (tptp.hAPP tptp.nat tptp.nat tptp.suc J))))))))))
% 10.23/10.45 (assume a482 (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.ord X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F B)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) C_1) B)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F Y_2)) (tptp.hAPP X_c X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F C_1)) A_2)))))))))
% 10.23/10.45 (assume a483 (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z $$unsorted) (Y $$unsorted)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_2) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_2) Z)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) Z)))))))
% 10.23/10.45 (assume a484 (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (=> (forall ((W $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) W)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) W) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) W) Z))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) Z))))))))
% 10.23/10.45 (assume a485 (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F B)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) C_1) B)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F Y_2)) (tptp.hAPP X_c X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F C_1)) A_2)))))))))
% 10.23/10.45 (assume a486 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (F $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) (tptp.hAPP X_c X_b F B))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) B) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_c X_b F X_2)) (tptp.hAPP X_c X_b F Y_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) (tptp.hAPP X_c X_b F C_1))))))))))
% 10.23/10.45 (assume a487 (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) B) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) C_1) (tptp.hAPP X_b X_c F B))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F Y_2)) (tptp.hAPP X_b X_c F X_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) C_1) (tptp.hAPP X_b X_c F A_2))))))))))
% 10.23/10.45 (assume a488 (forall ((X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_c)) (forall ((C_1 $$unsorted) (F $$unsorted) (B $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) B) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) C_1) (tptp.hAPP X_b X_c F B))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F Y_2)) (tptp.hAPP X_b X_c F X_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) C_1) (tptp.hAPP X_b X_c F A_2))))))))))
% 10.23/10.45 (assume a489 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (F $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) (tptp.hAPP X_c X_b F B))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) B) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_c X_b F X_2)) (tptp.hAPP X_c X_b F Y_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) (tptp.hAPP X_c X_b F C_1))))))))))
% 10.23/10.45 (assume a490 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) B)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F B)) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c F Y_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F A_2)) C_1)))))))))
% 10.23/10.45 (assume a491 (forall ((X_b $$unsorted) (X_c $$unsorted)) (=> (and (tptp.order X_c) (tptp.order X_b)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) A_2) B)) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less_eq X_c) (tptp.hAPP X_b X_c F B)) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F X_2)) (tptp.hAPP X_b X_c F Y_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_c (tptp.fun X_c tptp.bool) (tptp.ord_less X_c) (tptp.hAPP X_b X_c F A_2)) C_1)))))))))
% 10.23/10.45 (assume a492 (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) B_2)) (= (tptp.hAPP (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) tptp.nat (tptp.finite_card (tptp.sum_sum X_b X_c)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool)) (tptp.sum_Plus X_b X_c) A_3) B_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.nat (tptp.finite_card X_c) B_2)))))))
% 10.23/10.45 (assume a493 (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) tptp.bool (tptp.finite_finite (tptp.sum_sum X_b X_c)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool)) (tptp.sum_Plus X_b X_c) A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) B_2))))))
% 10.23/10.45 (assume a494 (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) tptp.bool (tptp.finite_finite (tptp.sum_sum X_b X_c)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool)) (tptp.sum_Plus X_b X_c) A_3) B_2)))))))
% 10.23/10.45 (assume a495 (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) tptp.bool (tptp.finite_finite (tptp.sum_sum X_b X_c)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool)) (tptp.sum_Plus X_b X_c) A_3) B_2))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)))))
% 10.23/10.45 (assume a496 (forall ((X_b $$unsorted) (X_c $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) tptp.bool (tptp.finite_finite (tptp.sum_sum X_b X_c)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool)) (tptp.sum_Plus X_b X_c) A_3) B_2))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) B_2)))))
% 10.23/10.45 (assume a497 (forall ((X_c $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (= (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool)) (tptp.sum_Plus X_b X_c) A_3) B_2) (tptp.bot_bot (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool))) (and (= (tptp.ti (tptp.fun X_b tptp.bool) A_3) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun X_c tptp.bool) B_2) (tptp.bot_bot (tptp.fun X_c tptp.bool)))))))
% 10.23/10.45 (assume a498 (forall ((X_c $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (and (=> (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) B_2))) (= (tptp.hAPP (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) tptp.nat (tptp.finite_card (tptp.sum_sum X_b X_c)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool)) (tptp.sum_Plus X_b X_c) A_3) B_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3)) (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.nat (tptp.finite_card X_c) B_2)))) (=> (not (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.finite_finite X_c) B_2)))) (= (tptp.hAPP (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) tptp.nat (tptp.finite_card (tptp.sum_sum X_b X_c)) (tptp.hAPP (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_c tptp.bool) (tptp.fun (tptp.sum_sum X_b X_c) tptp.bool)) (tptp.sum_Plus X_b X_c) A_3) B_2)) (tptp.zero_zero tptp.nat))))))
% 10.23/10.45 (assume a499 (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))))
% 10.23/10.45 (assume a500 (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))))
% 10.23/10.45 (assume a501 (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))
% 10.23/10.45 (assume a502 (forall ((X_b $$unsorted) (A_3 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.finite_finite X_b) A_3))) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) A_3) (tptp.zero_zero tptp.nat)))))
% 10.23/10.45 (assume a503 (forall ((X_b $$unsorted)) (= (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.nat (tptp.finite_card X_b) (tptp.bot_bot (tptp.fun X_b tptp.bool))) (tptp.zero_zero tptp.nat))))
% 10.23/10.45 (assume a504 (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))))
% 10.23/10.45 (assume a505 (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))))
% 10.23/10.45 (assume a506 (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))
% 10.23/10.45 (assume a507 (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))))
% 10.23/10.45 (assume a508 (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))))
% 10.23/10.45 (assume a509 (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.one_one X_a) (tptp.zero_zero X_a))))))
% 10.23/10.45 (assume a510 (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.zero_zero X_a) (tptp.one_one X_a))))))
% 10.23/10.45 (assume a511 (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) A_2)))))))
% 10.23/10.45 (assume a512 (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2)) (tptp.zero_zero X_b))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) (tptp.zero_zero X_b))))))))
% 10.23/10.45 (assume a513 (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B_1)))))))))
% 10.23/10.45 (assume a514 (forall ((X_b $$unsorted)) (=> (tptp.ordere216010020id_add X_b) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) X_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) Y_1)) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) X_1) Y_1) (tptp.zero_zero X_b)) (and (= (tptp.ti X_b X_1) (tptp.zero_zero X_b)) (= (tptp.ti X_b Y_1) (tptp.zero_zero X_b))))))))))
% 10.23/10.45 (assume a515 (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))
% 10.23/10.45 (assume a516 (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))
% 10.23/10.45 (assume a517 (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B_1 $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B_1)) (tptp.zero_zero X_a)))))))))
% 10.23/10.45 (assume a518 (forall ((X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) A_2) B)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B)) (tptp.zero_zero X_b))))))))
% 10.23/10.45 (assume a519 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) Na) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) (or (and (= M_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) (= Na (tptp.zero_zero tptp.nat))) (and (= M_1 (tptp.zero_zero tptp.nat)) (= Na (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))))))
% 10.23/10.45 (assume a520 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M_1) Na)) (or (and (= M_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) (= Na (tptp.zero_zero tptp.nat))) (and (= M_1 (tptp.zero_zero tptp.nat)) (= Na (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))))))
% 10.23/10.45 (assume a521 (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)) (tptp.zero_zero tptp.nat))))
% 10.23/10.45 (assume a522 (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N) (tptp.zero_zero tptp.nat)))))
% 10.23/10.45 (assume a523 (forall ((M_1 $$unsorted) (Na $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M_1) Na) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_1) Na)))))
% 10.23/10.45 (assume a524 (= (tptp.one_one tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))
% 10.23/10.45 (assume a525 (forall ((M $$unsorted) (N $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N) (tptp.zero_zero tptp.nat)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) M) (tptp.zero_zero tptp.nat)) (= M N)))))
% 10.23/10.45 (assume a526 (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) M) (tptp.zero_zero tptp.nat))))
% 10.23/10.45 (assume a527 (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) (tptp.zero_zero tptp.nat)) M)))
% 10.23/10.45 (assume a528 (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.zero_zero tptp.nat)) N) (tptp.zero_zero tptp.nat))))
% 10.23/10.45 (assume a529 (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))))
% 10.23/10.45 (assume a530 (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) A_1) (tptp.zero_zero X_a))))))
% 10.23/10.45 (assume a531 (forall ((X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (= (tptp.ti X_b A_2) (tptp.ti X_b B)) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B) (tptp.zero_zero X_b)))))))
% 10.23/10.45 (assume a532 (forall ((X_b $$unsorted)) (=> (tptp.group_add X_b) (forall ((A_2 $$unsorted) (B $$unsorted)) (= (= (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) A_2) B) (tptp.zero_zero X_b)) (= (tptp.ti X_b A_2) (tptp.ti X_b B)))))))
% 10.23/10.45 (assume a533 (forall ((M $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M) (tptp.zero_zero tptp.nat)))))
% 10.23/10.45 (assume a534 (forall ((M $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))))
% 10.23/10.45 (assume a535 (forall ((Nat_1 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_1) (tptp.zero_zero tptp.nat)))))
% 10.23/10.45 (assume a536 (forall ((M $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M) (tptp.zero_zero tptp.nat)))))
% 10.23/10.45 (assume a537 (forall ((Nat $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat)))))
% 10.23/10.45 (assume a538 (forall ((M $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))))
% 10.23/10.45 (assume a539 (forall ((X_b $$unsorted)) (=> (tptp.zero X_b) (forall ((X_1 $$unsorted)) (= (= (tptp.zero_zero X_b) (tptp.ti X_b X_1)) (= (tptp.ti X_b X_1) (tptp.zero_zero X_b)))))))
% 10.23/10.45 (assume a540 (= (tptp.bot_bot tptp.nat) (tptp.zero_zero tptp.nat)))
% 10.23/10.45 (assume a541 (forall ((Na $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Na) (tptp.zero_zero tptp.nat))) (= Na (tptp.zero_zero tptp.nat)))))
% 10.23/10.45 (assume a542 (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))))
% 10.23/10.45 (assume a543 (forall ((X_b $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (= (tptp.hAPP tptp.nat X_b (tptp.hAPP (tptp.fun tptp.nat X_b) (tptp.fun tptp.nat X_b) (tptp.hAPP X_b (tptp.fun (tptp.fun tptp.nat X_b) (tptp.fun tptp.nat X_b)) (tptp.nat_case X_b) F1) F2) (tptp.zero_zero tptp.nat)) (tptp.ti X_b F1))))
% 10.23/10.45 (assume a544 (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))))
% 10.23/10.45 (assume a545 (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))))
% 10.23/10.45 (assume a546 (forall ((X_b $$unsorted)) (=> (tptp.linord219039673up_add X_b) (forall ((A_2 $$unsorted)) (= (= (tptp.zero_zero X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.plus_plus X_b) A_2) A_2)) (= (tptp.ti X_b A_2) (tptp.zero_zero X_b)))))))
% 10.23/10.45 (assume a547 (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))))
% 10.23/10.45 (assume a548 (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))))
% 10.23/10.45 (assume a549 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.preorder T_1) (tptp.preorder (tptp.fun T_2 T_1)))))
% 10.23/10.45 (assume a550 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite_1 T_1) (tptp.finite_finite_1 T_2)) (tptp.finite_finite_1 (tptp.fun T_2 T_1)))))
% 10.23/10.45 (assume a551 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.order T_1) (tptp.order (tptp.fun T_2 T_1)))))
% 10.23/10.45 (assume a552 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.ord T_1) (tptp.ord (tptp.fun T_2 T_1)))))
% 10.23/10.45 (assume a553 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.bot T_1) (tptp.bot (tptp.fun T_2 T_1)))))
% 10.23/10.45 (assume a554 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.minus T_1) (tptp.minus (tptp.fun T_2 T_1)))))
% 10.23/10.45 (assume a555 (tptp.ordere223160158up_add tptp.nat))
% 10.23/10.45 (assume a556 (tptp.ordere236663937imp_le tptp.nat))
% 10.23/10.45 (assume a557 (tptp.ordere779506340up_add tptp.nat))
% 10.23/10.45 (assume a558 (tptp.ordere216010020id_add tptp.nat))
% 10.23/10.45 (assume a559 (tptp.cancel146912293up_add tptp.nat))
% 10.23/10.45 (assume a560 (tptp.cancel_semigroup_add tptp.nat))
% 10.23/10.45 (assume a561 (tptp.linordered_semidom tptp.nat))
% 10.23/10.45 (assume a562 (tptp.ab_semigroup_add tptp.nat))
% 10.23/10.45 (assume a563 (tptp.comm_monoid_add tptp.nat))
% 10.23/10.45 (assume a564 (tptp.zero_neq_one tptp.nat))
% 10.23/10.45 (assume a565 (tptp.preorder tptp.nat))
% 10.23/10.45 (assume a566 (tptp.linorder tptp.nat))
% 10.23/10.45 (assume a567 (tptp.monoid_add tptp.nat))
% 10.23/10.45 (assume a568 (tptp.order tptp.nat))
% 10.23/10.45 (assume a569 (tptp.ord tptp.nat))
% 10.23/10.45 (assume a570 (tptp.bot tptp.nat))
% 10.23/10.45 (assume a571 (tptp.minus tptp.nat))
% 10.23/10.45 (assume a572 (tptp.zero tptp.nat))
% 10.23/10.45 (assume a573 (tptp.one tptp.nat))
% 10.23/10.45 (assume a574 (tptp.preorder tptp.bool))
% 10.23/10.45 (assume a575 (tptp.finite_finite_1 tptp.bool))
% 10.23/10.45 (assume a576 (tptp.order tptp.bool))
% 10.23/10.45 (assume a577 (tptp.ord tptp.bool))
% 10.23/10.45 (assume a578 (tptp.bot tptp.bool))
% 10.23/10.45 (assume a579 (tptp.minus tptp.bool))
% 10.23/10.45 (assume a580 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite_1 T_1) (tptp.finite_finite_1 T_2)) (tptp.finite_finite_1 (tptp.sum_sum T_2 T_1)))))
% 10.23/10.45 (assume a581 (forall ((T $$unsorted) (A $$unsorted)) (= (tptp.ti T (tptp.ti T A)) (tptp.ti T A))))
% 10.23/10.45 (assume a582 (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P))) (not (tptp.hBOOL P)))))
% 10.23/10.45 (assume a583 (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P)))))
% 10.23/10.45 (assume a584 (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_a X_c) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c)) (tptp.combb X_b X_c X_a) P) Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))))
% 10.23/10.45 (assume a585 (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.hAPP X_b (tptp.fun X_a X_c) (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun X_b (tptp.fun X_a X_c)) (tptp.combc X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a (tptp.fun X_b X_c) P R) Q))))
% 10.23/10.45 (assume a586 (forall ((X_a $$unsorted) (P $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.combi X_a) P) (tptp.ti X_a P))))
% 10.23/10.45 (assume a587 (forall ((X_b $$unsorted) (X_a $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) (tptp.combk X_a X_b) P) Q) (tptp.ti X_a P))))
% 10.23/10.45 (assume a588 (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_a X_c) (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c)) (tptp.combs X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a (tptp.fun X_b X_c) P R) (tptp.hAPP X_a X_b Q R)))))
% 10.23/10.45 (assume a589 (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q)))))
% 10.23/10.45 (assume a590 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL P))))
% 10.23/10.45 (assume a591 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL Q))))
% 10.23/10.45 (assume a592 (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))))
% 10.23/10.45 (assume a593 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))))
% 10.23/10.45 (assume a594 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))))
% 10.23/10.45 (assume a595 (not (tptp.hBOOL tptp.fFalse)))
% 10.23/10.45 (assume a596 (forall ((P $$unsorted)) (or (= (tptp.ti tptp.bool P) tptp.fTrue) (= (tptp.ti tptp.bool P) tptp.fFalse))))
% 10.23/10.45 (assume a597 (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y))) (= (tptp.ti X_a X) (tptp.ti X_a Y)))))
% 10.23/10.45 (assume a598 (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y)))))
% 10.23/10.45 (assume a599 (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))))
% 10.23/10.45 (assume a600 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))))
% 10.23/10.45 (assume a601 (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))))
% 10.23/10.45 (assume a602 (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.finite_finite tptp.pname) tptp.u)))
% 10.23/10.45 (assume a603 (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))
% 10.23/10.45 (assume a604 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc tptp.na)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.nat (tptp.finite_card tptp.x_a) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))
% 10.23/10.45 (assume a605 (= (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.nat (tptp.finite_card tptp.x_a) tptp.g) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.nat (tptp.finite_card tptp.x_a) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hAPP tptp.nat tptp.nat tptp.suc tptp.na))))
% 10.23/10.45 (assume a606 (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u)))
% 10.23/10.45 (assume a607 (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g))))
% 10.23/10.45 (assume a608 (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))
% 10.23/10.45 (assume a609 true)
% 10.23/10.45 (step t1 (cl (=> (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))) :rule implies_neg1)
% 10.23/10.45 (anchor :step t2)
% 10.23/10.45 (assume t2.a0 (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))))
% 10.23/10.45 (step t2.t1 (cl (or (not (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule forall_inst :args ((:= X_c tptp.x_a) (:= X_b tptp.pname) (:= F tptp.mgt_call) (:= X_1 tptp.pn) (:= A_3 tptp.u)))
% 10.23/10.45 (step t2.t2 (cl (not (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) :rule or :premises (t2.t1))
% 10.23/10.45 (step t2.t3 (cl (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) :rule resolution :premises (t2.t2 t2.a0))
% 10.23/10.45 (step t2 (cl (not (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) :rule subproof :discharge (t2.a0))
% 10.23/10.45 (step t3 (cl (=> (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) :rule resolution :premises (t1 t2))
% 10.23/10.45 (step t4 (cl (=> (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) (not (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule implies_neg2)
% 10.23/10.45 (step t5 (cl (=> (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) (=> (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule resolution :premises (t3 t4))
% 10.23/10.45 (step t6 (cl (=> (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule contraction :premises (t5))
% 10.23/10.45 (step t7 (cl (not (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) :rule implies :premises (t6))
% 10.23/10.45 (step t8 (cl (not (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))) :rule or_pos)
% 10.23/10.45 (step t9 (cl (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (not (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule reordering :premises (t8))
% 10.23/10.45 (step t10 (cl (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))) (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))) (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) :rule and_neg)
% 10.23/10.45 (step t11 (cl (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))) (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) :rule reordering :premises (t10))
% 10.23/10.45 (step t12 (cl (not (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (not (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule equiv_pos1)
% 10.23/10.45 (step t13 (cl (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (not (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) (not (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))))) :rule reordering :premises (t12))
% 10.23/10.45 (step t14 (cl (=> (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))) :rule implies_neg1)
% 10.23/10.45 (anchor :step t15)
% 10.23/10.45 (assume t15.a0 (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2))))))
% 10.23/10.45 (step t15.t1 (cl (or (not (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))))) :rule forall_inst :args ((:= X_b tptp.x_a) (:= X_1 (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (:= A_3 tptp.g) (:= B_2 (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))
% 10.23/10.45 (step t15.t2 (cl (not (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule or :premises (t15.t1))
% 10.23/10.45 (step t15.t3 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule resolution :premises (t15.t2 t15.a0))
% 10.23/10.45 (step t15 (cl (not (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule subproof :discharge (t15.a0))
% 10.23/10.45 (step t16 (cl (=> (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule resolution :premises (t14 t15))
% 10.23/10.45 (step t17 (cl (=> (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) (not (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))))) :rule implies_neg2)
% 10.23/10.45 (step t18 (cl (=> (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) (=> (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))))) :rule resolution :premises (t16 t17))
% 10.23/10.45 (step t19 (cl (=> (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))))) :rule contraction :premises (t18))
% 10.23/10.45 (step t20 (cl (not (forall ((X_b $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool) (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_b tptp.bool)) (tptp.insert X_b) X_1) A_3)) B_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) B_2)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun X_b tptp.bool)) A_3) B_2)))))) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule implies :premises (t19))
% 10.23/10.45 (step t21 (cl (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.insert tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) tptp.g)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule resolution :premises (t20 a138))
% 10.23/10.45 (step t22 (cl (not (and (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.ord_less_eq (tptp.fun tptp.x_a tptp.bool)) tptp.g) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule resolution :premises (t13 a608 t21))
% 10.23/10.45 (step t23 (cl (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u))))) :rule resolution :premises (t11 a603 t22))
% 10.23/10.45 (step t24 (cl (not (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.pname tptp.bool) tptp.bool (tptp.hAPP tptp.pname (tptp.fun (tptp.fun tptp.pname tptp.bool) tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.x_a tptp.bool) tptp.bool (tptp.hAPP tptp.x_a (tptp.fun (tptp.fun tptp.x_a tptp.bool) tptp.bool) (tptp.member tptp.x_a) (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) (tptp.hAPP (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool) (tptp.hAPP (tptp.fun tptp.pname tptp.x_a) (tptp.fun (tptp.fun tptp.pname tptp.bool) (tptp.fun tptp.x_a tptp.bool)) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)))))) :rule resolution :premises (t9 a606 t23))
% 10.23/10.45 (step t25 (cl (not (= (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))))) (not (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))) :rule equiv_pos2)
% 10.23/10.47 (step t26 (cl (= (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3))))))) :rule all_simplify)
% 10.23/10.47 (step t27 (cl (forall ((X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.fun X_b tptp.bool) tptp.bool (tptp.hAPP X_b (tptp.fun (tptp.fun X_b tptp.bool) tptp.bool) (tptp.member X_b) X_1) A_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_c tptp.bool) tptp.bool (tptp.hAPP X_c (tptp.fun (tptp.fun X_c tptp.bool) tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c F X_1)) (tptp.hAPP (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool) (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_c tptp.bool)) (tptp.image X_b X_c) F) A_3)))))) :rule resolution :premises (t25 t26 a132))
% 10.23/10.47 (step t28 (cl) :rule resolution :premises (t7 t24 t27))
% 10.23/10.47
% 10.23/10.47 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.SVwWjdnxnN/cvc5---1.0.5_24393.smt2
% 10.23/10.47 % cvc5---1.0.5 exiting
% 10.23/10.48 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------