%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP077^1 : TPTP v9.2.1. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n016.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 Jun 3 08:24:59 AM UTC 2026 % Result : Theorem 0.80s 1.07s % Output : Proof 0.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP077^1 : TPTP v9.2.1. Released v7.5.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n016.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 04:14:09 EDT 2026 % 0.16/0.34 % CPUTime : % 0.37/0.62 %----Proving TH0 % 0.80/1.07 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.80/1.07 % SZS status Theorem % 0.80/1.07 % SZS output start Proof % 0.80/1.07 ( % 0.80/1.07 (declare-sort tptp.a 0) % 0.80/1.07 (declare-sort tptp.list_a 0) % 0.80/1.07 (declare-sort tptp.set_a 0) % 0.80/1.07 (declare-sort tptp.multiset_multiset_a 0) % 0.80/1.07 (declare-sort tptp.set_multiset_a 0) % 0.80/1.07 (declare-sort tptp.multiset_set_a 0) % 0.80/1.07 (declare-sort tptp.set_set_a 0) % 0.80/1.07 (declare-sort tptp.multiset_a 0) % 0.80/1.07 (declare-sort tptp.list_set_a 0) % 0.80/1.07 (declare-sort tptp.nat 0) % 0.80/1.07 (declare-sort tptp.set_list_a 0) % 0.80/1.07 (declare-sort tptp.set_nat 0) % 0.80/1.07 (declare-sort tptp.set_multiset_list_a 0) % 0.80/1.07 (declare-sort tptp.set_list_set_a 0) % 0.80/1.07 (declare-sort tptp.list_list_a 0) % 0.80/1.07 (declare-sort tptp.set_list_list_a 0) % 0.80/1.07 (declare-sort tptp.list_nat 0) % 0.80/1.07 (declare-sort tptp.multiset_list_a 0) % 0.80/1.07 (declare-sort tptp.list_list_set_a 0) % 0.80/1.07 (declare-sort tptp.list_set_list_set_a 0) % 0.80/1.07 (declare-sort tptp.set_list_list_set_a 0) % 0.80/1.07 (declare-sort tptp.list_list_list_a 0) % 0.80/1.07 (declare-sort tptp.list_set_list_list_a 0) % 0.80/1.07 (declare-sort tptp.set_list_list_list_a 0) % 0.80/1.07 (declare-sort tptp.list_multiset_a 0) % 0.80/1.07 (declare-sort tptp.list_set_multiset_a 0) % 0.80/1.07 (declare-sort tptp.set_set_list_a 0) % 0.80/1.07 (declare-sort tptp.set_set_nat 0) % 0.80/1.07 (declare-sort tptp.list_set_set_a 0) % 0.80/1.07 (declare-sort tptp.list_set_list_a 0) % 0.80/1.07 (declare-sort tptp.list_set_nat 0) % 0.80/1.07 (declare-sort tptp.list_set_set_set_a 0) % 0.80/1.07 (declare-sort tptp.set_set_set_a 0) % 0.80/1.07 (declare-sort tptp.multiset_nat 0) % 0.80/1.07 (declare-sort tptp.multiset_set_set_a 0) % 0.80/1.07 (declare-sort tptp.set_list_multiset_a 0) % 0.80/1.07 (declare-sort tptp.set_list_nat 0) % 0.80/1.07 (declare-sort tptp.list_multiset_list_a 0) % 0.80/1.07 (declare-sort tptp.multis971982480list_a 0) % 0.80/1.07 (declare-sort tptp.list_set_set_list_a 0) % 0.80/1.07 (declare-sort tptp.set_list_set_list_a 0) % 0.80/1.07 (declare-sort tptp.set_list_set_set_a 0) % 0.80/1.07 (declare-sort tptp.multiset_set_list_a 0) % 0.80/1.07 (declare-const tptp.listset_a (-> tptp.list_set_a tptp.set_list_a)) % 0.80/1.07 (declare-const tptp.groups1792256535list_a (-> tptp.list_a tptp.a)) % 0.80/1.07 (declare-const tptp.member_list_a (-> tptp.list_a tptp.set_list_a Bool)) % 0.80/1.07 (declare-const tptp.member_a (-> tptp.a tptp.set_a Bool)) % 0.80/1.07 (declare-const tptp.member_nat (-> tptp.nat tptp.set_nat Bool)) % 0.80/1.07 (declare-const tptp.nth_a (-> tptp.list_a tptp.nat tptp.a)) % 0.80/1.07 (declare-const tptp.size_size_list_a (-> tptp.list_a tptp.nat)) % 0.80/1.07 (declare-const tptp.ord_less_eq_nat (-> tptp.nat tptp.nat Bool)) % 0.80/1.07 (declare-const tptp.nth_set_a (-> tptp.list_set_a tptp.nat tptp.set_a)) % 0.80/1.07 (declare-const tptp.size_size_list_set_a (-> tptp.list_set_a tptp.nat)) % 0.80/1.07 (declare-const tptp.member_list_list_a (-> tptp.list_list_a tptp.set_list_list_a Bool)) % 0.80/1.07 (declare-const tptp.comm_m2145643721iset_a (-> tptp.multiset_multiset_a tptp.multiset_a)) % 0.80/1.07 (declare-const tptp.size_s577819178et_nat (-> tptp.list_set_nat tptp.nat)) % 0.80/1.07 (declare-const tptp.nth_set_nat (-> tptp.list_set_nat tptp.nat tptp.set_nat)) % 0.80/1.07 (declare-const tptp.size_s726512144_set_a (-> tptp.list_set_set_set_a tptp.nat)) % 0.80/1.07 (declare-const tptp.member814963949_set_a (-> tptp.list_set_set_a tptp.set_list_set_set_a Bool)) % 0.80/1.07 (declare-const tptp.mset_multiset_list_a (-> tptp.list_multiset_list_a tptp.multis971982480list_a)) % 0.80/1.07 (declare-const tptp.size_s469631926list_a (-> tptp.list_set_set_list_a tptp.nat)) % 0.80/1.07 (declare-const tptp.member101195155list_a (-> tptp.list_set_list_a tptp.set_list_set_list_a Bool)) % 0.80/1.07 (declare-const tptp.mset_list_a (-> tptp.list_list_a tptp.multiset_list_a)) % 0.80/1.07 (declare-const tptp.nth_set_set_a (-> tptp.list_set_set_a tptp.nat tptp.set_set_a)) % 0.80/1.07 (declare-const tptp.nth_set_list_a (-> tptp.list_set_list_a tptp.nat tptp.set_list_a)) % 0.80/1.07 (declare-const tptp.mset_set_set_a (-> tptp.list_set_set_a tptp.multiset_set_set_a)) % 0.80/1.07 (declare-const tptp.member_multiset_a (-> tptp.multiset_a tptp.set_multiset_a Bool)) % 0.80/1.07 (declare-const tptp.mset_set_list_a (-> tptp.list_set_list_a tptp.multiset_set_list_a)) % 0.80/1.07 (declare-const tptp.member528267379list_a (-> tptp.multiset_list_a tptp.set_multiset_list_a Bool)) % 0.80/1.07 (declare-const tptp.nth_set_set_list_a (-> tptp.list_set_set_list_a tptp.nat tptp.set_set_list_a)) % 0.80/1.07 (declare-const tptp.size_s1427607542list_a (-> tptp.list_list_a tptp.nat)) % 0.80/1.07 (declare-const tptp.perm_set_a (-> tptp.list_set_a tptp.list_set_a Bool)) % 0.80/1.07 (declare-const tptp.listset_set_a (-> tptp.list_set_set_a tptp.set_list_set_a)) % 0.80/1.07 (declare-const tptp.rev_list_a (-> tptp.list_list_a tptp.list_list_a)) % 0.80/1.07 (declare-const tptp.rev_set_a (-> tptp.list_set_a tptp.list_set_a)) % 0.80/1.07 (declare-const tptp.mset_set_a (-> tptp.list_set_a tptp.multiset_set_a)) % 0.80/1.07 (declare-const tptp.comm_m543484931mset_a (-> tptp.multiset_a tptp.a)) % 0.80/1.07 (declare-const tptp.member_list_nat (-> tptp.list_nat tptp.set_list_nat Bool)) % 0.80/1.07 (declare-const tptp.listset_multiset_a (-> tptp.list_set_multiset_a tptp.set_list_multiset_a)) % 0.80/1.07 (declare-const tptp.member518144627iset_a (-> tptp.list_multiset_a tptp.set_list_multiset_a Bool)) % 0.80/1.07 (declare-const tptp.comm_m1100186507et_nat (-> tptp.multiset_nat tptp.nat)) % 0.80/1.07 (declare-const tptp.groups1592617181iset_a (-> tptp.list_multiset_a tptp.multiset_a)) % 0.80/1.07 (declare-const tptp.ss1 tptp.list_set_a) % 0.80/1.07 (declare-const tptp.image_list_nat_nat (-> (-> tptp.list_nat tptp.nat) tptp.set_list_nat tptp.set_nat)) % 0.80/1.07 (declare-const tptp.groups921905271st_nat (-> tptp.list_nat tptp.nat)) % 0.80/1.07 (declare-const tptp.listset_set_set_a (-> tptp.list_set_set_set_a tptp.set_list_set_set_a)) % 0.80/1.07 (declare-const tptp.mset_multiset_a (-> tptp.list_multiset_a tptp.multiset_multiset_a)) % 0.80/1.07 (declare-const tptp.member_list_set_a (-> tptp.list_set_a tptp.set_list_set_a Bool)) % 0.80/1.07 (declare-const tptp.size_size_list_nat (-> tptp.list_nat tptp.nat)) % 0.80/1.07 (declare-const tptp.set_mset_a (-> tptp.multiset_a tptp.set_a)) % 0.80/1.07 (declare-const tptp.mset_nat (-> tptp.list_nat tptp.multiset_nat)) % 0.80/1.07 (declare-const tptp.comm_m324867663list_a (-> tptp.multis971982480list_a tptp.multiset_list_a)) % 0.80/1.07 (declare-const tptp.member954073875_set_a (-> tptp.list_list_set_a tptp.set_list_list_set_a Bool)) % 0.80/1.07 (declare-const tptp.nth_set_set_set_a (-> tptp.list_set_set_set_a tptp.nat tptp.set_set_set_a)) % 0.80/1.07 (declare-const tptp.a2 tptp.set_a) % 0.80/1.07 (declare-const tptp.qs2 tptp.list_a) % 0.80/1.07 (declare-const tptp.ss2 tptp.list_set_a) % 0.80/1.07 (declare-const tptp.groups1271887971list_a (-> tptp.list_multiset_list_a tptp.multiset_list_a)) % 0.80/1.07 (declare-const tptp.image_list_a_a (-> (-> tptp.list_a tptp.a) tptp.set_list_a tptp.set_a)) % 0.80/1.07 (declare-const tptp.rev_nat (-> tptp.list_nat tptp.list_nat)) % 0.80/1.07 (declare-const tptp.nth_list_a (-> tptp.list_list_a tptp.nat tptp.list_a)) % 0.80/1.07 (declare-const tptp.collect_list_set_a (-> (-> tptp.list_set_a Bool) tptp.set_list_set_a)) % 0.80/1.07 (declare-const tptp.mset_a (-> tptp.list_a tptp.multiset_a)) % 0.80/1.07 (declare-const tptp.member_set_list_a (-> tptp.set_list_a tptp.set_set_list_a Bool)) % 0.80/1.07 (declare-const tptp.hilber1014902394mp_nat (-> tptp.set_nat tptp.list_set_nat Bool)) % 0.80/1.07 (declare-const tptp.size_s341332310_set_a (-> tptp.list_list_set_a tptp.nat)) % 0.80/1.07 (declare-const tptp.size_s1635937238list_a (-> tptp.list_set_list_a tptp.nat)) % 0.80/1.07 (declare-const tptp.hilber2024005914iset_a (-> tptp.set_multiset_a tptp.list_set_multiset_a Bool)) % 0.80/1.07 (declare-const tptp.inj_on_a_list_a (-> (-> tptp.a tptp.list_a) tptp.set_a Bool)) % 0.80/1.07 (declare-const tptp.g (-> tptp.nat tptp.nat)) % 0.80/1.07 (declare-const tptp.size_s575106428list_a (-> tptp.list_list_list_a tptp.nat)) % 0.80/1.07 (declare-const tptp.size_s739728560_set_a (-> tptp.list_set_set_a tptp.nat)) % 0.80/1.07 (declare-const tptp.rev_a (-> tptp.list_a tptp.list_a)) % 0.80/1.07 (declare-const tptp.member1511395513list_a (-> tptp.list_list_list_a tptp.set_list_list_list_a Bool)) % 0.80/1.07 (declare-const tptp.set_ord_lessThan_nat (-> tptp.nat tptp.set_nat)) % 0.80/1.07 (declare-const tptp.listset_nat (-> tptp.list_set_nat tptp.set_list_nat)) % 0.80/1.07 (declare-const tptp.listset_list_a (-> tptp.list_set_list_a tptp.set_list_list_a)) % 0.80/1.07 (declare-const tptp.nth_nat (-> tptp.list_nat tptp.nat tptp.nat)) % 0.80/1.07 (declare-const tptp.listset_set_list_a (-> tptp.list_set_set_list_a tptp.set_list_set_list_a)) % 0.80/1.07 (declare-const tptp.rev_set_list_a (-> tptp.list_set_list_a tptp.list_set_list_a)) % 0.80/1.07 (declare-const tptp.rev_set_set_a (-> tptp.list_set_set_a tptp.list_set_set_a)) % 0.80/1.07 (declare-const tptp.ord_less_set_nat (-> tptp.set_nat tptp.set_nat Bool)) % 0.80/1.07 (declare-const tptp.set_or1597314339et_nat (-> tptp.set_nat tptp.set_set_nat)) % 0.80/1.07 (declare-const tptp.member_set_nat (-> tptp.set_nat tptp.set_set_nat Bool)) % 0.80/1.07 (declare-const tptp.set_mset_list_a (-> tptp.multiset_list_a tptp.set_list_a)) % 0.80/1.07 (declare-const tptp.ord_less_set_list_a (-> tptp.set_list_a tptp.set_list_a Bool)) % 0.80/1.07 (declare-const tptp.set_or1578766727list_a (-> tptp.set_list_a tptp.set_set_list_a)) % 0.80/1.07 (declare-const tptp.ord_less_set_a (-> tptp.set_a tptp.set_a Bool)) % 0.80/1.07 (declare-const tptp.set_or1164043265_set_a (-> tptp.set_a tptp.set_set_a)) % 0.80/1.07 (declare-const tptp.inj_on_list_a_list_a (-> (-> tptp.list_a tptp.list_a) tptp.set_list_a Bool)) % 0.80/1.07 (declare-const tptp.member_set_a (-> tptp.set_a tptp.set_set_a Bool)) % 0.80/1.07 (declare-const tptp.set_mset_multiset_a (-> tptp.multiset_multiset_a tptp.set_multiset_a)) % 0.80/1.07 (declare-const tptp.nth_set_multiset_a (-> tptp.list_set_multiset_a tptp.nat tptp.set_multiset_a)) % 0.80/1.07 (declare-const tptp.nth_multiset_a (-> tptp.list_multiset_a tptp.nat tptp.multiset_a)) % 0.80/1.07 (declare-const tptp.size_s802269334iset_a (-> tptp.list_set_multiset_a tptp.nat)) % 0.80/1.07 (declare-const tptp.size_s1657263798iset_a (-> tptp.list_multiset_a tptp.nat)) % 0.80/1.07 (declare-const tptp.listset_list_list_a (-> tptp.list_set_list_list_a tptp.set_list_list_list_a)) % 0.80/1.07 (declare-const tptp.nth_set_list_list_a (-> tptp.list_set_list_list_a tptp.nat tptp.set_list_list_a)) % 0.80/1.07 (declare-const tptp.collect_multiset_a (-> (-> tptp.multiset_a Bool) tptp.set_multiset_a)) % 0.80/1.07 (declare-const tptp.nth_list_list_a (-> tptp.list_list_list_a tptp.nat tptp.list_list_a)) % 0.80/1.07 (declare-const tptp.size_s240404444list_a (-> tptp.list_set_list_list_a tptp.nat)) % 0.80/1.07 (declare-const tptp.listset_list_set_a (-> tptp.list_set_list_set_a tptp.set_list_list_set_a)) % 0.80/1.07 (declare-const tptp.nth_set_list_set_a (-> tptp.list_set_list_set_a tptp.nat tptp.set_list_set_a)) % 0.80/1.07 (declare-const tptp.nth_list_set_a (-> tptp.list_list_set_a tptp.nat tptp.list_set_a)) % 0.80/1.07 (declare-const tptp.size_s926492982_set_a (-> tptp.list_set_list_set_a tptp.nat)) % 0.80/1.07 (declare-const tptp.set_ms1660427399list_a (-> tptp.multis971982480list_a tptp.set_multiset_list_a)) % 0.80/1.07 (declare-const tptp.f (-> tptp.nat tptp.nat)) % 0.80/1.07 (declare-const tptp.qs tptp.list_a) % 0.80/1.07 (declare-const tptp.inj_on_a_a (-> (-> tptp.a tptp.a) tptp.set_a Bool)) % 0.80/1.07 (declare-const tptp.collect_list_list_a (-> (-> tptp.list_list_a Bool) tptp.set_list_list_a)) % 0.80/1.07 (declare-const tptp.collect_set_a (-> (-> tptp.set_a Bool) tptp.set_set_a)) % 0.80/1.07 (declare-const tptp.collect_nat (-> (-> tptp.nat Bool) tptp.set_nat)) % 0.80/1.07 (declare-const tptp.collect_a (-> (-> tptp.a Bool) tptp.set_a)) % 0.80/1.07 (declare-const tptp.collect_list_a (-> (-> tptp.list_a Bool) tptp.set_list_a)) % 0.80/1.07 (declare-const tptp.perm_a (-> tptp.list_a tptp.list_a Bool)) % 0.80/1.07 (declare-const tptp.hilber815131374at_nat (-> tptp.set_nat (-> tptp.nat tptp.nat) tptp.nat tptp.nat)) % 0.80/1.07 (declare-const tptp.image_a_a (-> (-> tptp.a tptp.a) tptp.set_a tptp.set_a)) % 0.80/1.07 (declare-const tptp.image_a_list_a (-> (-> tptp.a tptp.list_a) tptp.set_a tptp.set_list_a)) % 0.80/1.07 (declare-const tptp.image_list_a_list_a (-> (-> tptp.list_a tptp.list_a) tptp.set_list_a tptp.set_list_a)) % 0.80/1.07 (declare-const tptp.image_nat_nat (-> (-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat)) % 0.80/1.07 (declare-const tptp.size_size_multiset_a (-> tptp.multiset_a tptp.nat)) % 0.80/1.07 (declare-const tptp.size_s657334288_set_a (-> tptp.multiset_set_a tptp.nat)) % 0.80/1.07 (declare-const tptp.member_set_set_a (-> tptp.set_set_a tptp.set_set_set_a Bool)) % 0.80/1.07 (declare-const tptp.hilbert_inv_into_a_a (-> tptp.set_a (-> tptp.a tptp.a) tptp.a tptp.a)) % 0.80/1.07 (declare-const tptp.hilber2125729734st_a_a (-> tptp.set_list_a (-> tptp.list_a tptp.a) tptp.a tptp.list_a)) % 0.80/1.07 (declare-const tptp.hilber165648082list_a (-> tptp.set_a (-> tptp.a tptp.list_a) tptp.list_a tptp.a)) % 0.80/1.07 (declare-const tptp.hilber921249868list_a (-> tptp.set_list_a (-> tptp.list_a tptp.list_a) tptp.list_a tptp.list_a)) % 0.80/1.07 (declare-const tptp.inj_on_list_a_a (-> (-> tptp.list_a tptp.a) tptp.set_list_a Bool)) % 0.80/1.07 (declare-const tptp.list_update_a (-> tptp.list_a tptp.nat tptp.a tptp.list_a)) % 0.80/1.07 (declare-const tptp.list_update_set_a (-> tptp.list_set_a tptp.nat tptp.set_a tptp.list_set_a)) % 0.80/1.07 (declare-const tptp.set_mset_set_a (-> tptp.multiset_set_a tptp.set_set_a)) % 0.80/1.07 (declare-const tptp.ord_less_eq_set_nat (-> tptp.set_nat tptp.set_nat Bool)) % 0.80/1.07 (declare-const tptp.a3 tptp.a) % 0.80/1.07 (declare-const tptp.inj_on_nat_nat (-> (-> tptp.nat tptp.nat) tptp.set_nat Bool)) % 0.80/1.07 (define tptp.bij_betw_list_a_a () (let ((_let_1 (@var "X5" tptp.a))) (let ((_let_2 (@var "G3" (-> tptp.a tptp.list_a)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "F3" (-> tptp.list_a tptp.a)))) (let ((_let_5 (@var "A4" tptp.set_list_a))) (let ((_let_6 (@var "B3" tptp.set_a))) (let ((_let_7 (@var "X5" tptp.list_a))) (let ((_let_8 (_ _let_4 _let_7))) (lambda (@list _let_4 _let_5 _let_6) (exists (@list _let_2) (and (forall (@list _let_7) (=> (_ (_ tptp.member_list_a _let_7) _let_5) (and (_ (_ tptp.member_a _let_8) _let_6) (= (_ _let_2 _let_8) _let_7)))) (forall (@list _let_1) (=> (_ (_ tptp.member_a _let_1) _let_6) (and (_ (_ tptp.member_list_a _let_3) _let_5) (= (_ _let_4 _let_3) _let_1)))))))))))))))) % 0.80/1.07 (define tptp.hilber2037636820comp_a () (let ((_let_1 (@var "A4" tptp.set_a))) (let ((_let_2 (@var "Ss2" tptp.list_set_a))) (lambda (@list _let_1 _let_2) (_ (_ (_ tptp.bij_betw_list_a_a tptp.groups1792256535list_a) (_ tptp.listset_a _let_2)) _let_1))))) % 0.80/1.07 (define tptp.bij_betw_a_a () (let ((_let_1 (@var "X5" tptp.a))) (let ((_let_2 (@var "G3" (-> tptp.a tptp.a)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "F3" (-> tptp.a tptp.a)))) (let ((_let_5 (@var "A4" tptp.set_a))) (let ((_let_6 (@var "B3" tptp.set_a))) (let ((_let_7 (_ tptp.member_a _let_1))) (let ((_let_8 (@list _let_1))) (let ((_let_9 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_5 _let_6) (exists (@list _let_2) (and (forall _let_8 (=> (_ _let_7 _let_5) (and (_ (_ tptp.member_a _let_9) _let_6) (= (_ _let_2 _let_9) _let_1)))) (forall _let_8 (=> (_ _let_7 _let_6) (and (_ (_ tptp.member_a _let_3) _let_5) (= (_ _let_4 _let_3) _let_1))))))))))))))))) % 0.80/1.07 (define tptp.bij_betw_a_list_a () (let ((_let_1 (@var "X5" tptp.list_a))) (let ((_let_2 (@var "G3" (-> tptp.list_a tptp.a)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "F3" (-> tptp.a tptp.list_a)))) (let ((_let_5 (@var "A4" tptp.set_a))) (let ((_let_6 (@var "B3" tptp.set_list_a))) (let ((_let_7 (@var "X5" tptp.a))) (let ((_let_8 (_ _let_4 _let_7))) (lambda (@list _let_4 _let_5 _let_6) (exists (@list _let_2) (and (forall (@list _let_7) (=> (_ (_ tptp.member_a _let_7) _let_5) (and (_ (_ tptp.member_list_a _let_8) _let_6) (= (_ _let_2 _let_8) _let_7)))) (forall (@list _let_1) (=> (_ (_ tptp.member_list_a _let_1) _let_6) (and (_ (_ tptp.member_a _let_3) _let_5) (= (_ _let_4 _let_3) _let_1)))))))))))))))) % 0.80/1.07 (define tptp.bij_be94573046list_a () (let ((_let_1 (@var "X5" tptp.list_a))) (let ((_let_2 (@var "G3" (-> tptp.list_a tptp.list_a)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "F3" (-> tptp.list_a tptp.list_a)))) (let ((_let_5 (@var "A4" tptp.set_list_a))) (let ((_let_6 (@var "B3" tptp.set_list_a))) (let ((_let_7 (_ tptp.member_list_a _let_1))) (let ((_let_8 (@list _let_1))) (let ((_let_9 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_5 _let_6) (exists (@list _let_2) (and (forall _let_8 (=> (_ _let_7 _let_5) (and (_ (_ tptp.member_list_a _let_9) _let_6) (= (_ _let_2 _let_9) _let_1)))) (forall _let_8 (=> (_ _let_7 _let_6) (and (_ (_ tptp.member_list_a _let_3) _let_5) (= (_ _let_4 _let_3) _let_1))))))))))))))))) % 0.80/1.07 (define tptp.bij_betw_nat_nat () (let ((_let_1 (@var "X5" tptp.nat))) (let ((_let_2 (@var "G3" (-> tptp.nat tptp.nat)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "F3" (-> tptp.nat tptp.nat)))) (let ((_let_5 (@var "A4" tptp.set_nat))) (let ((_let_6 (@var "B3" tptp.set_nat))) (let ((_let_7 (_ tptp.member_nat _let_1))) (let ((_let_8 (@list _let_1))) (let ((_let_9 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_5 _let_6) (exists (@list _let_2) (and (forall _let_8 (=> (_ _let_7 _let_5) (and (_ (_ tptp.member_nat _let_9) _let_6) (= (_ _let_2 _let_9) _let_1)))) (forall _let_8 (=> (_ _let_7 _let_6) (and (_ (_ tptp.member_nat _let_3) _let_5) (= (_ _let_4 _let_3) _let_1))))))))))))))))) % 0.80/1.07 (define tptp.ord_less_nat () (let ((_let_1 (@var "B5" tptp.nat))) (let ((_let_2 (@var "A7" tptp.nat))) (lambda (@list _let_1 _let_2) (and (_ (_ tptp.ord_less_eq_nat _let_1) _let_2) (not (= _let_2 _let_1))))))) % 0.80/1.07 (define tptp.list_ex_a () (let ((_let_1 (@var "N2" tptp.nat))) (let ((_let_2 (@var "Xs4" tptp.list_a))) (let ((_let_3 (@var "P2" (-> tptp.a Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ (_ tptp.ord_less_nat _let_1) (_ tptp.size_size_list_a _let_2)) (_ _let_3 (_ (_ tptp.nth_a _let_2) _let_1))))))))) % 0.80/1.07 (define tptp.list_ex_set_a () (let ((_let_1 (@var "N2" tptp.nat))) (let ((_let_2 (@var "Xs4" tptp.list_set_a))) (let ((_let_3 (@var "P2" (-> tptp.set_a Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ (_ tptp.ord_less_nat _let_1) (_ tptp.size_size_list_set_a _let_2)) (_ _let_3 (_ (_ tptp.nth_set_a _let_2) _let_1))))))))) % 0.80/1.07 (define tptp.ord_less_eq_set_a () (let ((_let_1 (@var "B3" tptp.set_a))) (let ((_let_2 (@var "T2" tptp.a))) (let ((_let_3 (_ tptp.member_a _let_2))) (let ((_let_4 (@var "A4" tptp.set_a))) (lambda (@list _let_4 _let_1) (forall (@list _let_2) (=> (_ _let_3 _let_4) (_ _let_3 _let_1))))))))) % 0.80/1.07 (define tptp.ord_le1301786372list_a () (let ((_let_1 (@var "B3" tptp.set_list_a))) (let ((_let_2 (@var "T2" tptp.list_a))) (let ((_let_3 (_ tptp.member_list_a _let_2))) (let ((_let_4 (@var "A4" tptp.set_list_a))) (lambda (@list _let_4 _let_1) (forall (@list _let_2) (=> (_ _let_3 _let_4) (_ _let_3 _let_1))))))))) % 0.80/1.07 (define tptp.ord_less_eq_o_nat () (let ((_let_1 (@var "Y4" (-> Bool tptp.nat)))) (let ((_let_2 (@var "X7" (-> Bool tptp.nat)))) (lambda (@list _let_2 _let_1) (and (_ (_ tptp.ord_less_eq_nat (_ _let_2 false)) (_ _let_1 false)) (_ (_ tptp.ord_less_eq_nat (_ _let_2 true)) (_ _let_1 true))))))) % 0.80/1.07 (define @t1 () (_ tptp.mset_a tptp.qs)) % 0.80/1.07 (define @t2 () (_ tptp.mset_a tptp.qs2)) % 0.80/1.07 (define @t3 () (= @t2 @t1)) % 0.80/1.07 (define @t4 () (_ tptp.groups1792256535list_a tptp.qs)) % 0.80/1.07 (define @t5 () (_ tptp.size_size_list_a tptp.qs)) % 0.80/1.07 (define @t6 () (_ tptp.size_size_list_a tptp.qs2)) % 0.80/1.07 (define @t7 () (_ tptp.listset_a tptp.ss1)) % 0.80/1.07 (define @t8 () (@var "Qs" tptp.list_a)) % 0.80/1.07 (define @t9 () (_ tptp.member_list_a @t8)) % 0.80/1.07 (define @t10 () (_ tptp.groups1792256535list_a @t8)) % 0.80/1.07 (define @t11 () (@list @t8)) % 0.80/1.07 (define @t12 () (_ tptp.listset_a tptp.ss2)) % 0.80/1.07 (define @t13 () (@var "A" tptp.set_multiset_a)) % 0.80/1.07 (define @t14 () (@var "Qs2" tptp.list_multiset_a)) % 0.80/1.07 (define @t15 () (@var "Ss" tptp.list_set_multiset_a)) % 0.80/1.07 (define @t16 () (_ tptp.listset_multiset_a @t15)) % 0.80/1.07 (define @t17 () (_ (_ tptp.hilber2024005914iset_a @t13) @t15)) % 0.80/1.07 (define @t18 () (@var "A" tptp.set_nat)) % 0.80/1.07 (define @t19 () (@var "Qs2" tptp.list_nat)) % 0.80/1.07 (define @t20 () (_ tptp.groups921905271st_nat @t19)) % 0.80/1.07 (define @t21 () (@var "Ss" tptp.list_set_nat)) % 0.80/1.07 (define @t22 () (_ tptp.listset_nat @t21)) % 0.80/1.07 (define @t23 () (_ (_ tptp.member_list_nat @t19) @t22)) % 0.80/1.07 (define @t24 () (_ (_ tptp.hilber1014902394mp_nat @t18) @t21)) % 0.80/1.07 (define @t25 () (@var "A" tptp.set_a)) % 0.80/1.07 (define @t26 () (@var "Qs2" tptp.list_a)) % 0.80/1.07 (define @t27 () (_ tptp.groups1792256535list_a @t26)) % 0.80/1.07 (define @t28 () (@var "Ss" tptp.list_set_a)) % 0.80/1.07 (define @t29 () (_ tptp.listset_a @t28)) % 0.80/1.07 (define @t30 () (_ (_ tptp.member_list_a @t26) @t29)) % 0.80/1.07 (define @t31 () (_ (_ tptp.hilber2037636820comp_a @t25) @t28)) % 0.80/1.07 (define @t32 () (@var "Qs" tptp.list_multiset_a)) % 0.80/1.07 (define @t33 () (_ tptp.groups1592617181iset_a @t32)) % 0.80/1.07 (define @t34 () (@var "A2" tptp.multiset_a)) % 0.80/1.07 (define @t35 () (_ (_ tptp.member518144627iset_a @t32) @t16)) % 0.80/1.07 (define @t36 () (@list @t32)) % 0.80/1.07 (define @t37 () (_ tptp.member_multiset_a @t34)) % 0.80/1.07 (define @t38 () (@var "Qs" tptp.list_nat)) % 0.80/1.07 (define @t39 () (_ tptp.groups921905271st_nat @t38)) % 0.80/1.07 (define @t40 () (@var "A2" tptp.nat)) % 0.80/1.07 (define @t41 () (_ (_ tptp.member_list_nat @t38) @t22)) % 0.80/1.07 (define @t42 () (@list @t38)) % 0.80/1.07 (define @t43 () (_ tptp.member_nat @t40)) % 0.80/1.07 (define @t44 () (_ @t43 @t18)) % 0.80/1.07 (define @t45 () (@var "A2" tptp.a)) % 0.80/1.07 (define @t46 () (_ @t9 @t29)) % 0.80/1.07 (define @t47 () (_ tptp.member_a @t45)) % 0.80/1.07 (define @t48 () (_ @t47 @t25)) % 0.80/1.07 (define @t49 () (@var "X" tptp.list_multiset_a)) % 0.80/1.07 (define @t50 () (@var "Y" tptp.list_multiset_a)) % 0.80/1.07 (define @t51 () (@var "A3" tptp.multiset_a)) % 0.80/1.07 (define @t52 () (@var "X" tptp.list_nat)) % 0.80/1.07 (define @t53 () (@var "Y" tptp.list_nat)) % 0.80/1.07 (define @t54 () (@var "A3" tptp.nat)) % 0.80/1.07 (define @t55 () (_ (_ tptp.member_nat @t54) @t18)) % 0.80/1.07 (define @t56 () (@list @t54)) % 0.80/1.07 (define @t57 () (@var "X" tptp.list_a)) % 0.80/1.07 (define @t58 () (@var "Y" tptp.list_a)) % 0.80/1.07 (define @t59 () (@var "A3" tptp.a)) % 0.80/1.07 (define @t60 () (@list @t28 @t25)) % 0.80/1.07 (define @t61 () (@var "Qs3" tptp.list_nat)) % 0.80/1.07 (define @t62 () (@var "Qs3" tptp.list_a)) % 0.80/1.07 (define @t63 () (@var "Xs" tptp.list_nat)) % 0.80/1.07 (define @t64 () (_ tptp.groups921905271st_nat @t63)) % 0.80/1.07 (define @t65 () (_ tptp.rev_nat @t63)) % 0.80/1.07 (define @t66 () (@list @t63)) % 0.80/1.07 (define @t67 () (@var "Xs" tptp.list_a)) % 0.80/1.07 (define @t68 () (_ tptp.groups1792256535list_a @t67)) % 0.80/1.07 (define @t69 () (_ tptp.rev_a @t67)) % 0.80/1.07 (define @t70 () (@list @t67)) % 0.80/1.07 (define @t71 () (@var "I" tptp.nat)) % 0.80/1.07 (define @t72 () (_ tptp.g @t71)) % 0.80/1.07 (define @t73 () (_ tptp.nth_a tptp.qs)) % 0.80/1.07 (define @t74 () (_ tptp.ord_less_nat @t71)) % 0.80/1.07 (define @t75 () (@list @t71)) % 0.80/1.07 (define @t76 () (_ tptp.bij_betw_nat_nat tptp.g)) % 0.80/1.07 (define @t77 () (_ tptp.mset_nat @t63)) % 0.80/1.07 (define @t78 () (@var "Xs" tptp.list_multiset_list_a)) % 0.80/1.07 (define @t79 () (@var "Xs" tptp.list_multiset_a)) % 0.80/1.07 (define @t80 () (_ tptp.mset_a @t67)) % 0.80/1.07 (define @t81 () (_ tptp.comm_m543484931mset_a @t80)) % 0.80/1.07 (define @t82 () (forall @t70 (= @t81 @t68))) % 0.80/1.07 (define @t83 () (= (_ (_ tptp.image_list_a_a tptp.groups1792256535list_a) @t29) @t25)) % 0.80/1.07 (define @t84 () (@list @t25 @t28)) % 0.80/1.07 (define @t85 () (@var "Xs" tptp.list_set_a)) % 0.80/1.07 (define @t86 () (_ tptp.mset_set_a @t85)) % 0.80/1.07 (define @t87 () (_ tptp.rev_set_a @t85)) % 0.80/1.07 (define @t88 () (@list @t85)) % 0.80/1.07 (define @t89 () (@var "Xs" tptp.list_list_a)) % 0.80/1.07 (define @t90 () (_ tptp.mset_list_a @t89)) % 0.80/1.07 (define @t91 () (_ tptp.rev_list_a @t89)) % 0.80/1.07 (define @t92 () (@list @t89)) % 0.80/1.07 (define @t93 () (@var "I2" tptp.nat)) % 0.80/1.07 (define @t94 () (@var "Qs22" tptp.list_a)) % 0.80/1.07 (define @t95 () (_ tptp.ord_less_nat @t93)) % 0.80/1.07 (define @t96 () (@list @t93)) % 0.80/1.07 (define @t97 () (@var "X2" tptp.multiset_set_a)) % 0.80/1.07 (define @t98 () (@var "Xs2" tptp.list_set_a)) % 0.80/1.07 (define @t99 () (@list @t98)) % 0.80/1.07 (define @t100 () (@var "X2" tptp.multiset_list_a)) % 0.80/1.07 (define @t101 () (@var "Xs2" tptp.list_list_a)) % 0.80/1.07 (define @t102 () (@list @t101)) % 0.80/1.07 (define @t103 () (@var "X2" tptp.multiset_a)) % 0.80/1.07 (define @t104 () (@var "Xs2" tptp.list_a)) % 0.80/1.07 (define @t105 () (@list @t104)) % 0.80/1.07 (define @t106 () (@var "Ys" tptp.list_list_a)) % 0.80/1.07 (define @t107 () (_ tptp.size_s1427607542list_a @t106)) % 0.80/1.07 (define @t108 () (_ tptp.size_s1427607542list_a @t89)) % 0.80/1.07 (define @t109 () (= @t108 @t107)) % 0.80/1.07 (define @t110 () (= @t90 (_ tptp.mset_list_a @t106))) % 0.80/1.07 (define @t111 () (@list @t89 @t106)) % 0.80/1.07 (define @t112 () (@var "Ys" tptp.list_set_list_a)) % 0.80/1.07 (define @t113 () (_ tptp.size_s1635937238list_a @t112)) % 0.80/1.07 (define @t114 () (@var "Xs" tptp.list_set_list_a)) % 0.80/1.07 (define @t115 () (_ tptp.size_s1635937238list_a @t114)) % 0.80/1.07 (define @t116 () (= @t115 @t113)) % 0.80/1.07 (define @t117 () (= (_ tptp.mset_set_list_a @t114) (_ tptp.mset_set_list_a @t112))) % 0.80/1.07 (define @t118 () (@list @t114 @t112)) % 0.80/1.07 (define @t119 () (@var "Ys" tptp.list_set_set_a)) % 0.80/1.07 (define @t120 () (_ tptp.size_s739728560_set_a @t119)) % 0.80/1.07 (define @t121 () (@var "Xs" tptp.list_set_set_a)) % 0.80/1.07 (define @t122 () (_ tptp.size_s739728560_set_a @t121)) % 0.80/1.07 (define @t123 () (= @t122 @t120)) % 0.80/1.07 (define @t124 () (= (_ tptp.mset_set_set_a @t121) (_ tptp.mset_set_set_a @t119))) % 0.80/1.07 (define @t125 () (@list @t121 @t119)) % 0.80/1.07 (define @t126 () (@var "Ys" tptp.list_nat)) % 0.80/1.07 (define @t127 () (_ tptp.size_size_list_nat @t126)) % 0.80/1.07 (define @t128 () (_ tptp.size_size_list_nat @t63)) % 0.80/1.07 (define @t129 () (= @t128 @t127)) % 0.80/1.07 (define @t130 () (= @t77 (_ tptp.mset_nat @t126))) % 0.80/1.07 (define @t131 () (@list @t63 @t126)) % 0.80/1.07 (define @t132 () (@var "Ys" tptp.list_a)) % 0.80/1.07 (define @t133 () (_ tptp.size_size_list_a @t132)) % 0.80/1.07 (define @t134 () (_ tptp.size_size_list_a @t67)) % 0.80/1.07 (define @t135 () (= @t134 @t133)) % 0.80/1.07 (define @t136 () (= @t80 (_ tptp.mset_a @t132))) % 0.80/1.07 (define @t137 () (@list @t67 @t132)) % 0.80/1.07 (define @t138 () (@var "Ys" tptp.list_set_a)) % 0.80/1.07 (define @t139 () (_ tptp.size_size_list_set_a @t138)) % 0.80/1.07 (define @t140 () (_ tptp.size_size_list_set_a @t85)) % 0.80/1.07 (define @t141 () (= @t140 @t139)) % 0.80/1.07 (define @t142 () (= @t86 (_ tptp.mset_set_a @t138))) % 0.80/1.07 (define @t143 () (@list @t85 @t138)) % 0.80/1.07 (define @t144 () (@var "I3" tptp.nat)) % 0.80/1.07 (define @t145 () (@var "F" (-> tptp.nat tptp.nat))) % 0.80/1.07 (define @t146 () (_ @t145 @t144)) % 0.80/1.07 (define @t147 () (_ tptp.nth_list_a @t106)) % 0.80/1.07 (define @t148 () (_ (_ tptp.nth_list_a @t89) @t144)) % 0.80/1.07 (define @t149 () (_ tptp.ord_less_nat @t144)) % 0.80/1.07 (define @t150 () (_ @t149 @t108)) % 0.80/1.07 (define @t151 () (@list @t144)) % 0.80/1.07 (define @t152 () (_ tptp.bij_betw_nat_nat @t145)) % 0.80/1.07 (define @t153 () (_ tptp.nth_set_list_a @t112)) % 0.80/1.07 (define @t154 () (_ tptp.nth_set_list_a @t114)) % 0.80/1.07 (define @t155 () (_ @t154 @t144)) % 0.80/1.07 (define @t156 () (_ @t149 @t115)) % 0.80/1.07 (define @t157 () (_ @t152 (_ tptp.set_ord_lessThan_nat @t115))) % 0.80/1.07 (define @t158 () (_ tptp.nth_set_set_a @t119)) % 0.80/1.07 (define @t159 () (_ tptp.nth_set_set_a @t121)) % 0.80/1.07 (define @t160 () (_ @t159 @t144)) % 0.80/1.07 (define @t161 () (_ @t149 @t122)) % 0.80/1.07 (define @t162 () (_ @t152 (_ tptp.set_ord_lessThan_nat @t122))) % 0.80/1.07 (define @t163 () (_ tptp.nth_nat @t126)) % 0.80/1.07 (define @t164 () (_ (_ tptp.nth_nat @t63) @t144)) % 0.80/1.07 (define @t165 () (_ @t149 @t128)) % 0.80/1.07 (define @t166 () (_ tptp.nth_a @t132)) % 0.80/1.07 (define @t167 () (_ tptp.nth_a @t67)) % 0.80/1.07 (define @t168 () (_ @t167 @t144)) % 0.80/1.07 (define @t169 () (_ @t149 @t134)) % 0.80/1.07 (define @t170 () (_ tptp.set_ord_lessThan_nat @t133)) % 0.80/1.07 (define @t171 () (_ tptp.set_ord_lessThan_nat @t134)) % 0.80/1.07 (define @t172 () (_ tptp.nth_set_a @t138)) % 0.80/1.07 (define @t173 () (_ tptp.nth_set_a @t85)) % 0.80/1.07 (define @t174 () (_ @t173 @t144)) % 0.80/1.07 (define @t175 () (_ @t149 @t140)) % 0.80/1.07 (define @t176 () (_ tptp.set_ord_lessThan_nat @t139)) % 0.80/1.07 (define @t177 () (_ tptp.set_ord_lessThan_nat @t140)) % 0.80/1.07 (define @t178 () (_ @t152 @t177)) % 0.80/1.07 (define @t179 () (_ @t145 @t93)) % 0.80/1.07 (define @t180 () (@var "Ys2" tptp.list_set_list_a)) % 0.80/1.07 (define @t181 () (@var "Xs3" tptp.list_set_set_list_a)) % 0.80/1.07 (define @t182 () (@var "Xs" tptp.list_set_set_list_a)) % 0.80/1.07 (define @t183 () (_ tptp.nth_set_set_list_a @t182)) % 0.80/1.07 (define @t184 () (_ tptp.size_s469631926list_a @t182)) % 0.80/1.07 (define @t185 () (_ @t149 @t184)) % 0.80/1.07 (define @t186 () (_ (_ tptp.member101195155list_a @t112) (_ tptp.listset_set_list_a @t182))) % 0.80/1.07 (define @t187 () (@var "Ys2" tptp.list_set_set_a)) % 0.80/1.07 (define @t188 () (@var "Xs3" tptp.list_set_set_set_a)) % 0.80/1.07 (define @t189 () (@var "Xs" tptp.list_set_set_set_a)) % 0.80/1.07 (define @t190 () (_ tptp.nth_set_set_set_a @t189)) % 0.80/1.07 (define @t191 () (_ tptp.size_s726512144_set_a @t189)) % 0.80/1.07 (define @t192 () (_ @t149 @t191)) % 0.80/1.07 (define @t193 () (_ (_ tptp.member814963949_set_a @t119) (_ tptp.listset_set_set_a @t189))) % 0.80/1.07 (define @t194 () (@var "Ys2" tptp.list_nat)) % 0.80/1.08 (define @t195 () (@var "Xs3" tptp.list_set_nat)) % 0.80/1.08 (define @t196 () (@var "Xs" tptp.list_set_nat)) % 0.80/1.08 (define @t197 () (_ tptp.nth_set_nat @t196)) % 0.80/1.08 (define @t198 () (_ tptp.size_s577819178et_nat @t196)) % 0.80/1.08 (define @t199 () (_ @t149 @t198)) % 0.80/1.08 (define @t200 () (_ (_ tptp.member_list_nat @t126) (_ tptp.listset_nat @t196))) % 0.80/1.08 (define @t201 () (@var "Ys2" tptp.list_list_a)) % 0.80/1.08 (define @t202 () (@var "Xs3" tptp.list_set_list_a)) % 0.80/1.08 (define @t203 () (_ (_ tptp.member_list_list_a @t106) (_ tptp.listset_list_a @t114))) % 0.80/1.08 (define @t204 () (@var "Ys2" tptp.list_set_a)) % 0.80/1.08 (define @t205 () (@var "Xs3" tptp.list_set_set_a)) % 0.80/1.08 (define @t206 () (_ (_ tptp.member_list_set_a @t138) (_ tptp.listset_set_a @t121))) % 0.80/1.08 (define @t207 () (@var "Ys2" tptp.list_a)) % 0.80/1.08 (define @t208 () (@var "Xs3" tptp.list_set_a)) % 0.80/1.08 (define @t209 () (_ tptp.listset_a @t85)) % 0.80/1.08 (define @t210 () (_ (_ tptp.member_list_a @t132) @t209)) % 0.80/1.08 (define @t211 () (_ tptp.size_size_list_set_a tptp.ss2)) % 0.80/1.08 (define @t212 () (_ tptp.set_ord_lessThan_nat @t211)) % 0.80/1.08 (define @t213 () (_ tptp.size_size_list_set_a tptp.ss1)) % 0.80/1.08 (define @t214 () (_ tptp.set_ord_lessThan_nat @t213)) % 0.80/1.08 (define @t215 () (@var "K" tptp.set_nat)) % 0.80/1.08 (define @t216 () (@var "I" tptp.set_nat)) % 0.80/1.08 (define @t217 () (@var "K" tptp.set_list_a)) % 0.80/1.08 (define @t218 () (@var "I" tptp.set_list_a)) % 0.80/1.08 (define @t219 () (@var "K" tptp.set_a)) % 0.80/1.08 (define @t220 () (@var "I" tptp.set_a)) % 0.80/1.08 (define @t221 () (@var "K" tptp.nat)) % 0.80/1.08 (define @t222 () (@var "Xs" tptp.list_set_multiset_a)) % 0.80/1.08 (define @t223 () (@var "Ys" tptp.list_multiset_a)) % 0.80/1.08 (define @t224 () (_ (_ tptp.member518144627iset_a @t223) (_ tptp.listset_multiset_a @t222))) % 0.80/1.08 (define @t225 () (_ tptp.nth_set_multiset_a @t222)) % 0.80/1.08 (define @t226 () (_ tptp.nth_multiset_a @t223)) % 0.80/1.08 (define @t227 () (_ tptp.size_s802269334iset_a @t222)) % 0.80/1.08 (define @t228 () (@var "Xs" tptp.list_set_list_list_a)) % 0.80/1.08 (define @t229 () (@var "Ys" tptp.list_list_list_a)) % 0.80/1.08 (define @t230 () (_ (_ tptp.member1511395513list_a @t229) (_ tptp.listset_list_list_a @t228))) % 0.80/1.08 (define @t231 () (_ tptp.nth_set_list_list_a @t228)) % 0.80/1.08 (define @t232 () (_ tptp.nth_list_list_a @t229)) % 0.80/1.08 (define @t233 () (_ tptp.size_s240404444list_a @t228)) % 0.80/1.08 (define @t234 () (@var "Xs" tptp.list_set_list_set_a)) % 0.80/1.08 (define @t235 () (@var "Ys" tptp.list_list_set_a)) % 0.80/1.08 (define @t236 () (_ (_ tptp.member954073875_set_a @t235) (_ tptp.listset_list_set_a @t234))) % 0.80/1.08 (define @t237 () (_ tptp.nth_set_list_set_a @t234)) % 0.80/1.08 (define @t238 () (_ tptp.nth_list_set_a @t235)) % 0.80/1.08 (define @t239 () (_ tptp.size_s926492982_set_a @t234)) % 0.80/1.08 (define @t240 () (_ @t153 @t144)) % 0.80/1.08 (define @t241 () (_ @t158 @t144)) % 0.80/1.08 (define @t242 () (_ @t163 @t144)) % 0.80/1.08 (define @t243 () (_ @t147 @t144)) % 0.80/1.08 (define @t244 () (_ @t166 @t144)) % 0.80/1.08 (define @t245 () (= @t133 @t140)) % 0.80/1.08 (define @t246 () (@list @t132 @t85)) % 0.80/1.08 (define @t247 () (_ @t172 @t144)) % 0.80/1.08 (define @t248 () (= @t139 @t122)) % 0.80/1.08 (define @t249 () (@list @t138 @t121)) % 0.80/1.08 (define @t250 () (= @t89 @t106)) % 0.80/1.08 (define @t251 () (= @t114 @t112)) % 0.80/1.08 (define @t252 () (= @t121 @t119)) % 0.80/1.08 (define @t253 () (= @t63 @t126)) % 0.80/1.08 (define @t254 () (= @t67 @t132)) % 0.80/1.08 (define @t255 () (= @t85 @t138)) % 0.80/1.08 (define @t256 () (@var "I4" tptp.nat)) % 0.80/1.08 (define @t257 () (@var "Xs4" tptp.list_list_a)) % 0.80/1.08 (define @t258 () (_ (_ tptp.nth_list_a @t257) @t256)) % 0.80/1.08 (define @t259 () (@var "P" (-> tptp.nat tptp.list_a Bool))) % 0.80/1.08 (define @t260 () (_ @t259 @t256)) % 0.80/1.08 (define @t261 () (_ tptp.ord_less_nat @t256)) % 0.80/1.08 (define @t262 () (_ @t261 @t221)) % 0.80/1.08 (define @t263 () (@list @t256)) % 0.80/1.08 (define @t264 () (_ tptp.size_s1427607542list_a @t257)) % 0.80/1.08 (define @t265 () (@var "X3" tptp.list_a)) % 0.80/1.08 (define @t266 () (@var "Xs4" tptp.list_set_list_a)) % 0.80/1.08 (define @t267 () (_ (_ tptp.nth_set_list_a @t266) @t256)) % 0.80/1.08 (define @t268 () (@var "P" (-> tptp.nat tptp.set_list_a Bool))) % 0.80/1.08 (define @t269 () (_ @t268 @t256)) % 0.80/1.08 (define @t270 () (_ tptp.size_s1635937238list_a @t266)) % 0.80/1.08 (define @t271 () (@var "X3" tptp.set_list_a)) % 0.80/1.08 (define @t272 () (@var "Xs4" tptp.list_set_set_a)) % 0.80/1.08 (define @t273 () (_ (_ tptp.nth_set_set_a @t272) @t256)) % 0.80/1.08 (define @t274 () (@var "P" (-> tptp.nat tptp.set_set_a Bool))) % 0.80/1.08 (define @t275 () (_ @t274 @t256)) % 0.80/1.08 (define @t276 () (_ tptp.size_s739728560_set_a @t272)) % 0.80/1.08 (define @t277 () (@var "X3" tptp.set_set_a)) % 0.80/1.08 (define @t278 () (@var "Xs4" tptp.list_nat)) % 0.80/1.08 (define @t279 () (_ (_ tptp.nth_nat @t278) @t256)) % 0.80/1.08 (define @t280 () (@var "P" (-> tptp.nat tptp.nat Bool))) % 0.80/1.08 (define @t281 () (_ @t280 @t256)) % 0.80/1.08 (define @t282 () (_ tptp.size_size_list_nat @t278)) % 0.80/1.08 (define @t283 () (@var "X3" tptp.nat)) % 0.80/1.08 (define @t284 () (@list @t283)) % 0.80/1.08 (define @t285 () (@var "Xs4" tptp.list_a)) % 0.80/1.08 (define @t286 () (_ tptp.nth_a @t285)) % 0.80/1.08 (define @t287 () (_ @t286 @t256)) % 0.80/1.08 (define @t288 () (@var "P" (-> tptp.nat tptp.a Bool))) % 0.80/1.08 (define @t289 () (_ @t288 @t256)) % 0.80/1.08 (define @t290 () (_ tptp.size_size_list_a @t285)) % 0.80/1.08 (define @t291 () (@var "X3" tptp.a)) % 0.80/1.08 (define @t292 () (@var "Xs4" tptp.list_set_a)) % 0.80/1.08 (define @t293 () (_ tptp.nth_set_a @t292)) % 0.80/1.08 (define @t294 () (_ @t293 @t256)) % 0.80/1.08 (define @t295 () (@var "P" (-> tptp.nat tptp.set_a Bool))) % 0.80/1.08 (define @t296 () (_ @t295 @t256)) % 0.80/1.08 (define @t297 () (_ tptp.size_size_list_set_a @t292)) % 0.80/1.08 (define @t298 () (@var "X3" tptp.set_a)) % 0.80/1.08 (define @t299 () (@var "Ys3" tptp.list_list_a)) % 0.80/1.08 (define @t300 () (@var "Z" tptp.list_list_a)) % 0.80/1.08 (define @t301 () (@var "Y2" tptp.list_list_a)) % 0.80/1.08 (define @t302 () (@var "Ys3" tptp.list_set_list_a)) % 0.80/1.08 (define @t303 () (@var "Z" tptp.list_set_list_a)) % 0.80/1.08 (define @t304 () (@var "Y2" tptp.list_set_list_a)) % 0.80/1.08 (define @t305 () (@var "Ys3" tptp.list_set_set_a)) % 0.80/1.08 (define @t306 () (@var "Z" tptp.list_set_set_a)) % 0.80/1.08 (define @t307 () (@var "Y2" tptp.list_set_set_a)) % 0.80/1.08 (define @t308 () (@var "Ys3" tptp.list_nat)) % 0.80/1.08 (define @t309 () (@var "Z" tptp.list_nat)) % 0.80/1.08 (define @t310 () (@var "Y2" tptp.list_nat)) % 0.80/1.08 (define @t311 () (@var "Ys3" tptp.list_a)) % 0.80/1.08 (define @t312 () (@var "Z" tptp.list_a)) % 0.80/1.08 (define @t313 () (@var "Y2" tptp.list_a)) % 0.80/1.08 (define @t314 () (@var "Ys3" tptp.list_set_a)) % 0.80/1.08 (define @t315 () (@var "Z" tptp.list_set_a)) % 0.80/1.08 (define @t316 () (@var "Y2" tptp.list_set_a)) % 0.80/1.08 (define @t317 () (@var "Y3" tptp.nat)) % 0.80/1.08 (define @t318 () (@var "X4" tptp.nat)) % 0.80/1.08 (define @t319 () (= @t318 @t317)) % 0.80/1.08 (define @t320 () (_ tptp.set_ord_lessThan_nat @t317)) % 0.80/1.08 (define @t321 () (_ tptp.set_ord_lessThan_nat @t318)) % 0.80/1.08 (define @t322 () (@list @t318 @t317)) % 0.80/1.08 (define @t323 () (_ tptp.rev_a @t132)) % 0.80/1.08 (define @t324 () (_ tptp.rev_set_a @t138)) % 0.80/1.08 (define @t325 () (_ tptp.nth_set_a tptp.ss1)) % 0.80/1.08 (define @t326 () (_ tptp.nth_set_a tptp.ss2)) % 0.80/1.08 (define @t327 () (_ @t74 @t213)) % 0.80/1.08 (define @t328 () (_ tptp.f @t71)) % 0.80/1.08 (define @t329 () (_ @t74 @t211)) % 0.80/1.08 (define @t330 () (@var "F2" (-> tptp.nat tptp.nat))) % 0.80/1.08 (define @t331 () (_ @t330 @t93)) % 0.80/1.08 (define @t332 () (= (_ @t325 @t93) (_ @t326 @t331))) % 0.80/1.08 (define @t333 () (_ tptp.bij_betw_nat_nat @t330)) % 0.80/1.08 (define @t334 () (@list @t330)) % 0.80/1.08 (define @t335 () (_ @t173 @t71)) % 0.80/1.08 (define @t336 () (_ @t74 @t140)) % 0.80/1.08 (define @t337 () (@var "P" (-> tptp.multiset_a Bool))) % 0.80/1.08 (define @t338 () (@var "A2" tptp.list_list_a)) % 0.80/1.08 (define @t339 () (@var "P" (-> tptp.list_list_a Bool))) % 0.80/1.08 (define @t340 () (@var "A2" tptp.list_set_a)) % 0.80/1.08 (define @t341 () (@var "P" (-> tptp.list_set_a Bool))) % 0.80/1.08 (define @t342 () (@var "A2" tptp.set_a)) % 0.80/1.08 (define @t343 () (@var "P" (-> tptp.set_a Bool))) % 0.80/1.08 (define @t344 () (@var "P" (-> tptp.nat Bool))) % 0.80/1.08 (define @t345 () (_ @t344 @t40)) % 0.80/1.08 (define @t346 () (@var "P" (-> tptp.a Bool))) % 0.80/1.08 (define @t347 () (_ tptp.collect_a @t346)) % 0.80/1.08 (define @t348 () (@var "A2" tptp.list_a)) % 0.80/1.08 (define @t349 () (@var "P" (-> tptp.list_a Bool))) % 0.80/1.08 (define @t350 () (_ tptp.collect_list_a @t349)) % 0.80/1.08 (define @t351 () (_ tptp.member_list_a @t348)) % 0.80/1.08 (define @t352 () (@var "X5" tptp.multiset_a)) % 0.80/1.08 (define @t353 () (@var "A" tptp.set_list_list_a)) % 0.80/1.08 (define @t354 () (@var "X5" tptp.list_list_a)) % 0.80/1.08 (define @t355 () (@var "A" tptp.set_list_set_a)) % 0.80/1.08 (define @t356 () (@var "X5" tptp.list_set_a)) % 0.80/1.08 (define @t357 () (@var "A" tptp.set_set_a)) % 0.80/1.08 (define @t358 () (@var "X5" tptp.set_a)) % 0.80/1.08 (define @t359 () (@var "X5" tptp.nat)) % 0.80/1.08 (define @t360 () (_ tptp.member_nat @t359)) % 0.80/1.08 (define @t361 () (@list @t359)) % 0.80/1.08 (define @t362 () (@var "X5" tptp.a)) % 0.80/1.08 (define @t363 () (_ tptp.member_a @t362)) % 0.80/1.08 (define @t364 () (@list @t362)) % 0.80/1.08 (define @t365 () (@var "A" tptp.set_list_a)) % 0.80/1.08 (define @t366 () (@var "X5" tptp.list_a)) % 0.80/1.08 (define @t367 () (_ tptp.member_list_a @t366)) % 0.80/1.08 (define @t368 () (@list @t366)) % 0.80/1.08 (define @t369 () (@var "Q" (-> tptp.list_a Bool))) % 0.80/1.08 (define @t370 () (@var "X6" tptp.list_a)) % 0.80/1.08 (define @t371 () (_ @t349 @t370)) % 0.80/1.08 (define @t372 () (@list @t370)) % 0.80/1.08 (define @t373 () (@var "Q" (-> tptp.a Bool))) % 0.80/1.08 (define @t374 () (@var "X6" tptp.a)) % 0.80/1.08 (define @t375 () (@list @t374)) % 0.80/1.08 (define @t376 () (@var "N" tptp.nat)) % 0.80/1.08 (define @t377 () (@list @t376)) % 0.80/1.08 (define @t378 () (@var "Xs2" tptp.list_set_list_a)) % 0.80/1.08 (define @t379 () (_ tptp.size_s1635937238list_a @t378)) % 0.80/1.08 (define @t380 () (@list @t378)) % 0.80/1.08 (define @t381 () (@var "Xs2" tptp.list_set_set_a)) % 0.80/1.08 (define @t382 () (_ tptp.size_s739728560_set_a @t381)) % 0.80/1.08 (define @t383 () (@list @t381)) % 0.80/1.08 (define @t384 () (@var "Xs2" tptp.list_nat)) % 0.80/1.08 (define @t385 () (_ tptp.size_size_list_nat @t384)) % 0.80/1.08 (define @t386 () (@list @t384)) % 0.80/1.08 (define @t387 () (_ tptp.size_size_list_a @t104)) % 0.80/1.08 (define @t388 () (_ tptp.size_size_list_set_a @t98)) % 0.80/1.08 (define @t389 () (@var "M" tptp.nat)) % 0.80/1.08 (define @t390 () (@var "P" (-> tptp.list_set_list_a Bool))) % 0.80/1.08 (define @t391 () (@var "Ys4" tptp.list_set_list_a)) % 0.80/1.08 (define @t392 () (@var "P" (-> tptp.list_set_set_a Bool))) % 0.80/1.08 (define @t393 () (@var "Ys4" tptp.list_set_set_a)) % 0.80/1.08 (define @t394 () (@var "P" (-> tptp.list_nat Bool))) % 0.80/1.08 (define @t395 () (@var "Ys4" tptp.list_nat)) % 0.80/1.08 (define @t396 () (@var "Ys4" tptp.list_a)) % 0.80/1.08 (define @t397 () (@var "Ys4" tptp.list_set_a)) % 0.80/1.08 (define @t398 () (_ (_ tptp.perm_a @t67) @t132)) % 0.80/1.08 (define @t399 () (_ tptp.perm_set_a @t85)) % 0.80/1.08 (define @t400 () (_ @t399 @t138)) % 0.80/1.08 (define @t401 () (@var "L" tptp.list_set_a)) % 0.80/1.08 (define @t402 () (@var "F" (-> tptp.a tptp.a))) % 0.80/1.08 (define @t403 () (_ (_ tptp.image_a_a @t402) @t25)) % 0.80/1.08 (define @t404 () (@var "B" tptp.a)) % 0.80/1.08 (define @t405 () (_ tptp.member_a @t404)) % 0.80/1.08 (define @t406 () (_ @t405 @t403)) % 0.80/1.08 (define @t407 () (@var "X4" tptp.a)) % 0.80/1.08 (define @t408 () (_ tptp.member_a @t407)) % 0.80/1.08 (define @t409 () (_ @t408 @t25)) % 0.80/1.08 (define @t410 () (_ @t402 @t407)) % 0.80/1.08 (define @t411 () (= @t404 @t410)) % 0.80/1.08 (define @t412 () (@var "F" (-> tptp.a tptp.list_a))) % 0.80/1.08 (define @t413 () (_ (_ tptp.image_a_list_a @t412) @t25)) % 0.80/1.08 (define @t414 () (@var "B" tptp.list_a)) % 0.80/1.08 (define @t415 () (_ tptp.member_list_a @t414)) % 0.80/1.08 (define @t416 () (_ @t415 @t413)) % 0.80/1.08 (define @t417 () (_ @t412 @t407)) % 0.80/1.08 (define @t418 () (= @t414 @t417)) % 0.80/1.08 (define @t419 () (@var "F" (-> tptp.list_a tptp.a))) % 0.80/1.08 (define @t420 () (_ (_ tptp.image_list_a_a @t419) @t365)) % 0.80/1.08 (define @t421 () (_ @t405 @t420)) % 0.80/1.08 (define @t422 () (@var "X4" tptp.list_a)) % 0.80/1.08 (define @t423 () (_ tptp.member_list_a @t422)) % 0.80/1.08 (define @t424 () (_ @t423 @t365)) % 0.80/1.08 (define @t425 () (_ @t419 @t422)) % 0.80/1.08 (define @t426 () (= @t404 @t425)) % 0.80/1.08 (define @t427 () (@var "F" (-> tptp.list_a tptp.list_a))) % 0.80/1.08 (define @t428 () (_ (_ tptp.image_list_a_list_a @t427) @t365)) % 0.80/1.08 (define @t429 () (_ @t415 @t428)) % 0.80/1.08 (define @t430 () (_ @t427 @t422)) % 0.80/1.08 (define @t431 () (= @t414 @t430)) % 0.80/1.08 (define @t432 () (@var "B2" tptp.set_nat)) % 0.80/1.08 (define @t433 () (_ tptp.image_nat_nat @t145)) % 0.80/1.08 (define @t434 () (_ @t433 @t18)) % 0.80/1.08 (define @t435 () (= @t434 @t432)) % 0.80/1.08 (define @t436 () (_ @t152 @t18)) % 0.80/1.08 (define @t437 () (_ @t436 @t432)) % 0.80/1.08 (define @t438 () (@list @t145 @t18 @t432)) % 0.80/1.08 (define @t439 () (@var "Y3" tptp.list_a)) % 0.80/1.08 (define @t440 () (_ tptp.size_size_list_a @t422)) % 0.80/1.08 (define @t441 () (@var "Y3" tptp.list_set_a)) % 0.80/1.08 (define @t442 () (@var "X4" tptp.list_set_a)) % 0.80/1.08 (define @t443 () (_ tptp.size_size_list_set_a @t442)) % 0.80/1.08 (define @t444 () (_ (_ tptp.member_list_set_a @t442) @t355)) % 0.80/1.08 (define @t445 () (@var "B2" tptp.set_a)) % 0.80/1.08 (define @t446 () (@var "C" tptp.a)) % 0.80/1.08 (define @t447 () (_ tptp.member_a @t446)) % 0.80/1.08 (define @t448 () (=> (_ @t447 @t25) (_ @t447 @t445))) % 0.80/1.08 (define @t449 () (@list @t25 @t445 @t446)) % 0.80/1.08 (define @t450 () (@var "B2" tptp.set_list_a)) % 0.80/1.08 (define @t451 () (@var "C" tptp.list_a)) % 0.80/1.08 (define @t452 () (_ tptp.member_list_a @t451)) % 0.80/1.08 (define @t453 () (=> (_ @t452 @t365) (_ @t452 @t450))) % 0.80/1.08 (define @t454 () (@list @t365 @t450 @t451)) % 0.80/1.08 (define @t455 () (@var "X" tptp.nat)) % 0.80/1.08 (define @t456 () (@list @t455)) % 0.80/1.08 (define @t457 () (@var "G" (-> tptp.nat tptp.nat))) % 0.80/1.08 (define @t458 () (@var "A5" tptp.set_nat)) % 0.80/1.08 (define @t459 () (@var "G2" (-> tptp.nat tptp.nat))) % 0.80/1.08 (define @t460 () (_ @t436 @t458)) % 0.80/1.08 (define @t461 () (_ tptp.member_a (_ @t402 @t45))) % 0.80/1.08 (define @t462 () (_ tptp.member_list_a (_ @t412 @t45))) % 0.80/1.08 (define @t463 () (_ tptp.member_a (_ @t419 @t348))) % 0.80/1.08 (define @t464 () (_ @t351 @t365)) % 0.80/1.08 (define @t465 () (_ tptp.member_list_a (_ @t427 @t348))) % 0.80/1.08 (define @t466 () (_ @t145 @t40)) % 0.80/1.08 (define @t467 () (_ tptp.perm_set_a @t138)) % 0.80/1.08 (define @t468 () (@var "Zs" tptp.list_set_a)) % 0.80/1.08 (define @t469 () (@var "A6" tptp.nat)) % 0.80/1.08 (define @t470 () (_ (_ tptp.hilber815131374at_nat @t18) @t145)) % 0.80/1.08 (define @t471 () (@list @t145 @t18 @t458 @t40)) % 0.80/1.08 (define @t472 () (_ tptp.bij_betw_nat_nat @t470)) % 0.80/1.08 (define @t473 () (_ (_ tptp.member_nat @t317) @t434)) % 0.80/1.08 (define @t474 () (_ tptp.member_nat @t318)) % 0.80/1.08 (define @t475 () (_ @t474 @t434)) % 0.80/1.08 (define @t476 () (_ @t470 @t317)) % 0.80/1.08 (define @t477 () (_ @t470 @t318)) % 0.80/1.08 (define @t478 () (_ (_ tptp.inj_on_list_a_a tptp.groups1792256535list_a) @t29)) % 0.80/1.08 (define @t479 () (@var "Ns" tptp.list_nat)) % 0.80/1.08 (define @t480 () (_ @t167 @t71)) % 0.80/1.08 (define @t481 () (@var "J" tptp.nat)) % 0.80/1.08 (define @t482 () (_ @t167 @t481)) % 0.80/1.08 (define @t483 () (_ (_ tptp.list_update_a @t67) @t71)) % 0.80/1.08 (define @t484 () (_ tptp.ord_less_nat @t481)) % 0.80/1.08 (define @t485 () (_ @t74 @t134)) % 0.80/1.08 (define @t486 () (_ @t173 @t481)) % 0.80/1.08 (define @t487 () (_ (_ tptp.list_update_set_a @t85) @t71)) % 0.80/1.08 (define @t488 () (@var "Ls" tptp.list_a)) % 0.80/1.08 (define @t489 () (_ tptp.mset_a @t488)) % 0.80/1.08 (define @t490 () (_ tptp.nth_a @t488)) % 0.80/1.08 (define @t491 () (_ @t490 @t71)) % 0.80/1.08 (define @t492 () (_ tptp.size_size_list_a @t488)) % 0.80/1.08 (define @t493 () (_ @t74 @t492)) % 0.80/1.08 (define @t494 () (@var "Ls" tptp.list_set_a)) % 0.80/1.08 (define @t495 () (_ tptp.mset_set_a @t494)) % 0.80/1.08 (define @t496 () (_ tptp.nth_set_a @t494)) % 0.80/1.08 (define @t497 () (_ @t496 @t71)) % 0.80/1.08 (define @t498 () (_ tptp.size_size_list_set_a @t494)) % 0.80/1.08 (define @t499 () (_ @t74 @t498)) % 0.80/1.08 (define @t500 () (@var "Ls" tptp.list_list_a)) % 0.80/1.08 (define @t501 () (@var "M2" tptp.multiset_a)) % 0.80/1.08 (define @t502 () (@var "MM" tptp.multiset_multiset_a)) % 0.80/1.08 (define @t503 () (@var "M2" tptp.multiset_list_a)) % 0.80/1.08 (define @t504 () (@var "MM" tptp.multis971982480list_a)) % 0.80/1.08 (define @t505 () (_ tptp.ord_less_eq_nat @t318)) % 0.80/1.08 (define @t506 () (_ @t505 @t317)) % 0.80/1.08 (define @t507 () (_ @t483 @t407)) % 0.80/1.08 (define @t508 () (= @t507 @t67)) % 0.80/1.08 (define @t509 () (@list @t67 @t71 @t407)) % 0.80/1.08 (define @t510 () (@var "X4" tptp.set_a)) % 0.80/1.08 (define @t511 () (_ @t487 @t510)) % 0.80/1.08 (define @t512 () (= @t511 @t85)) % 0.80/1.08 (define @t513 () (@list @t85 @t71 @t510)) % 0.80/1.08 (define @t514 () (_ @t145 @t318)) % 0.80/1.08 (define @t515 () (_ @t474 @t18)) % 0.80/1.08 (define @t516 () (_ (_ tptp.inj_on_nat_nat @t145) @t18)) % 0.80/1.08 (define @t517 () (_ tptp.nth_a @t507)) % 0.80/1.08 (define @t518 () (_ @t517 @t481)) % 0.80/1.08 (define @t519 () (= @t71 @t481)) % 0.80/1.08 (define @t520 () (not @t519)) % 0.80/1.08 (define @t521 () (=> @t520 (= @t518 @t482))) % 0.80/1.08 (define @t522 () (_ tptp.nth_set_a @t511)) % 0.80/1.08 (define @t523 () (_ @t522 @t481)) % 0.80/1.08 (define @t524 () (=> @t520 (= @t523 @t486))) % 0.80/1.08 (define @t525 () (@var "S" tptp.set_nat)) % 0.80/1.08 (define @t526 () (_ tptp.image_nat_nat @t470)) % 0.80/1.08 (define @t527 () (@list @t71 @t67 @t407)) % 0.80/1.08 (define @t528 () (@list @t71 @t85 @t510)) % 0.80/1.08 (define @t529 () (_ tptp.ord_less_eq_set_nat @t432)) % 0.80/1.08 (define @t530 () (_ (_ tptp.ord_less_eq_set_a @t25) @t445)) % 0.80/1.08 (define @t531 () (_ @t47 @t445)) % 0.80/1.08 (define @t532 () (_ (_ tptp.ord_le1301786372list_a @t365) @t450)) % 0.80/1.08 (define @t533 () (_ @t351 @t450)) % 0.80/1.08 (define @t534 () (_ tptp.member_a @t374)) % 0.80/1.08 (define @t535 () (_ @t534 @t25)) % 0.80/1.08 (define @t536 () (_ tptp.member_list_a @t370)) % 0.80/1.08 (define @t537 () (_ @t536 @t365)) % 0.80/1.08 (define @t538 () (@var "B3" tptp.set_nat)) % 0.80/1.08 (define @t539 () (@var "A4" tptp.set_nat)) % 0.80/1.08 (define @t540 () (@var "F3" (-> tptp.nat tptp.nat))) % 0.80/1.08 (define @t541 () (@list @t540 @t539 @t538)) % 0.80/1.08 (define @t542 () (@var "Xa" tptp.list_a)) % 0.80/1.08 (define @t543 () (_ tptp.size_size_list_a @t370)) % 0.80/1.08 (define @t544 () (@var "Xa" tptp.list_set_a)) % 0.80/1.08 (define @t545 () (@var "X6" tptp.list_set_a)) % 0.80/1.08 (define @t546 () (_ tptp.size_size_list_set_a @t545)) % 0.80/1.08 (define @t547 () (@var "B4" tptp.set_nat)) % 0.80/1.08 (define @t548 () (= (_ @t433 @t432) @t547)) % 0.80/1.08 (define @t549 () (_ @t529 @t18)) % 0.80/1.08 (define @t550 () (@list @t145 @t18 @t458 @t432 @t547)) % 0.80/1.08 (define @t551 () (@var "F4" (-> tptp.nat tptp.nat))) % 0.80/1.08 (define @t552 () (_ tptp.ord_less_eq_set_nat @t434)) % 0.80/1.08 (define @t553 () (@var "X6" tptp.nat)) % 0.80/1.08 (define @t554 () (_ tptp.member_nat @t553)) % 0.80/1.08 (define @t555 () (@list @t553)) % 0.80/1.08 (define @t556 () (_ @t145 @t553)) % 0.80/1.08 (define @t557 () (@var "H" (-> tptp.nat tptp.nat))) % 0.80/1.08 (define @t558 () (@list @t318)) % 0.80/1.08 (define @t559 () (@var "T" tptp.nat)) % 0.80/1.08 (define @t560 () (@var "Z2" tptp.nat)) % 0.80/1.08 (define @t561 () (_ tptp.ord_less_nat @t455)) % 0.80/1.08 (define @t562 () (_ @t561 @t560)) % 0.80/1.08 (define @t563 () (@list @t560)) % 0.80/1.08 (define @t564 () (@list @t559)) % 0.80/1.08 (define @t565 () (_ tptp.ord_less_eq_nat @t455)) % 0.80/1.08 (define @t566 () (@var "M4" tptp.nat)) % 0.80/1.08 (define @t567 () (_ @t344 @t455)) % 0.80/1.08 (define @t568 () (@var "M3" tptp.nat)) % 0.80/1.08 (define @t569 () (_ tptp.ord_less_eq_nat @t553)) % 0.80/1.08 (define @t570 () (_ @t344 @t553)) % 0.80/1.08 (define @t571 () (@var "B3" tptp.set_a)) % 0.80/1.08 (define @t572 () (_ @t363 @t571)) % 0.80/1.08 (define @t573 () (@var "A4" tptp.set_a)) % 0.80/1.08 (define @t574 () (_ @t363 @t573)) % 0.80/1.08 (define @t575 () (@list @t573 @t571)) % 0.80/1.08 (define @t576 () (@var "B3" tptp.set_list_a)) % 0.80/1.08 (define @t577 () (_ @t367 @t576)) % 0.80/1.08 (define @t578 () (@var "A4" tptp.set_list_a)) % 0.80/1.08 (define @t579 () (_ @t367 @t578)) % 0.80/1.08 (define @t580 () (@list @t578 @t576)) % 0.80/1.08 (define @t581 () (@var "B" tptp.nat)) % 0.80/1.08 (define @t582 () (= @t40 @t581)) % 0.80/1.08 (define @t583 () (_ tptp.ord_less_eq_nat @t40)) % 0.80/1.08 (define @t584 () (_ @t583 @t581)) % 0.80/1.08 (define @t585 () (_ tptp.ord_less_eq_nat @t581)) % 0.80/1.08 (define @t586 () (_ @t585 @t40)) % 0.80/1.08 (define @t587 () (@list @t581 @t40)) % 0.80/1.08 (define @t588 () (@var "B5" tptp.nat)) % 0.80/1.08 (define @t589 () (@var "A7" tptp.nat)) % 0.80/1.08 (define @t590 () (_ (_ tptp.ord_less_eq_nat @t589) @t588)) % 0.80/1.08 (define @t591 () (_ (_ tptp.ord_less_eq_nat @t588) @t589)) % 0.80/1.08 (define @t592 () (@list @t589 @t588)) % 0.80/1.08 (define @t593 () (@var "Z" tptp.nat)) % 0.80/1.08 (define @t594 () (@var "Y2" tptp.nat)) % 0.80/1.08 (define @t595 () (lambda (@list @t594 @t593) (= @t594 @t593))) % 0.80/1.08 (define @t596 () (@var "C" tptp.nat)) % 0.80/1.08 (define @t597 () (_ tptp.ord_less_eq_nat @t596)) % 0.80/1.08 (define @t598 () (_ @t597 @t581)) % 0.80/1.08 (define @t599 () (@list @t581 @t40 @t596)) % 0.80/1.08 (define @t600 () (@var "B6" tptp.nat)) % 0.80/1.08 (define @t601 () (_ @t280 @t54)) % 0.80/1.08 (define @t602 () (_ @t601 @t600)) % 0.80/1.08 (define @t603 () (@list @t54 @t600)) % 0.80/1.08 (define @t604 () (=> (forall @t603 (=> (_ (_ @t280 @t600) @t54) @t602)) (_ (_ @t280 @t40) @t581))) % 0.80/1.08 (define @t605 () (@list @t280 @t40 @t581)) % 0.80/1.08 (define @t606 () (@list @t40)) % 0.80/1.08 (define @t607 () (@var "Z3" tptp.nat)) % 0.80/1.08 (define @t608 () (_ @t505 @t607)) % 0.80/1.08 (define @t609 () (_ tptp.ord_less_eq_nat @t317)) % 0.80/1.08 (define @t610 () (_ @t609 @t607)) % 0.80/1.08 (define @t611 () (@list @t318 @t317 @t607)) % 0.80/1.08 (define @t612 () (@list @t40 @t581)) % 0.80/1.08 (define @t613 () (_ @t583 @t596)) % 0.80/1.08 (define @t614 () (= @t581 @t596)) % 0.80/1.08 (define @t615 () (@list @t40 @t581 @t596)) % 0.80/1.08 (define @t616 () (_ @t585 @t596)) % 0.80/1.08 (define @t617 () (=> @t616 @t613)) % 0.80/1.08 (define @t618 () (_ @t609 @t318)) % 0.80/1.08 (define @t619 () (@list @t317 @t318)) % 0.80/1.08 (define @t620 () (not @t506)) % 0.80/1.08 (define @t621 () (_ tptp.ord_less_eq_nat @t607)) % 0.80/1.08 (define @t622 () (_ @t621 @t318)) % 0.80/1.08 (define @t623 () (_ @t621 @t317)) % 0.80/1.08 (define @t624 () (@var "Y5" tptp.nat)) % 0.80/1.08 (define @t625 () (@var "Y" tptp.nat)) % 0.80/1.08 (define @t626 () (_ @t145 @t625)) % 0.80/1.08 (define @t627 () (@list @t553 @t625)) % 0.80/1.08 (define @t628 () (forall @t627 (=> (_ @t569 @t625) (_ (_ tptp.ord_less_eq_nat @t556) @t626)))) % 0.80/1.08 (define @t629 () (=> @t628 (_ (_ tptp.ord_less_eq_nat @t466) @t596))) % 0.80/1.08 (define @t630 () (_ @t145 @t581)) % 0.80/1.08 (define @t631 () (= @t630 @t596)) % 0.80/1.08 (define @t632 () (@list @t40 @t581 @t145 @t596)) % 0.80/1.08 (define @t633 () (_ @t145 @t596)) % 0.80/1.08 (define @t634 () (=> @t616 (=> @t628 (_ @t583 @t633)))) % 0.80/1.08 (define @t635 () (= @t40 @t630)) % 0.80/1.08 (define @t636 () (@list @t40 @t145 @t581 @t596)) % 0.80/1.08 (define @t637 () (not @t582)) % 0.80/1.08 (define @t638 () (_ tptp.ord_less_nat @t581)) % 0.80/1.08 (define @t639 () (_ @t638 @t40)) % 0.80/1.08 (define @t640 () (_ tptp.ord_less_nat @t40)) % 0.80/1.08 (define @t641 () (_ @t640 @t581)) % 0.80/1.08 (define @t642 () (_ tptp.ord_less_nat @t317)) % 0.80/1.08 (define @t643 () (_ @t642 @t318)) % 0.80/1.08 (define @t644 () (_ tptp.ord_less_nat @t318)) % 0.80/1.08 (define @t645 () (_ @t644 @t317)) % 0.80/1.08 (define @t646 () (not @t645)) % 0.80/1.08 (define @t647 () (_ tptp.ord_less_nat @t596)) % 0.80/1.08 (define @t648 () (_ @t647 @t40)) % 0.80/1.08 (define @t649 () (=> (_ @t647 @t581) @t648)) % 0.80/1.08 (define @t650 () (@var "M5" tptp.nat)) % 0.80/1.08 (define @t651 () (@var "P2" (-> tptp.nat Bool))) % 0.80/1.08 (define @t652 () (@var "N2" tptp.nat)) % 0.80/1.08 (define @t653 () (@list @t652)) % 0.80/1.08 (define @t654 () (@var "P3" (-> tptp.nat Bool))) % 0.80/1.08 (define @t655 () (not @t643)) % 0.80/1.08 (define @t656 () (_ @t640 @t596)) % 0.80/1.08 (define @t657 () (_ @t638 @t596)) % 0.80/1.08 (define @t658 () (=> @t657 @t656)) % 0.80/1.08 (define @t659 () (not @t319)) % 0.80/1.08 (define @t660 () (@var "P" Bool)) % 0.80/1.08 (define @t661 () (@var "Y6" tptp.nat)) % 0.80/1.08 (define @t662 () (@var "X_1" tptp.nat)) % 0.80/1.08 (define @t663 () (_ tptp.ord_less_nat @t553)) % 0.80/1.08 (define @t664 () (forall @t627 (=> (_ @t663 @t625) (_ (_ tptp.ord_less_nat @t556) @t626)))) % 0.80/1.08 (define @t665 () (=> @t664 (_ (_ tptp.ord_less_nat @t466) @t596))) % 0.80/1.08 (define @t666 () (=> @t657 (=> @t664 (_ @t640 @t633)))) % 0.80/1.08 (define @t667 () (@var "Q2" (-> tptp.nat Bool))) % 0.80/1.08 (define @t668 () (_ @t667 @t455)) % 0.80/1.08 (define @t669 () (@var "P4" (-> tptp.nat Bool))) % 0.80/1.08 (define @t670 () (_ @t669 @t455)) % 0.80/1.08 (define @t671 () (@var "Q" (-> tptp.nat Bool))) % 0.80/1.08 (define @t672 () (_ @t671 @t455)) % 0.80/1.08 (define @t673 () (= (and @t567 @t672) (and @t670 @t668))) % 0.80/1.08 (define @t674 () (_ (_ tptp.ord_less_nat @t560) @t455)) % 0.80/1.08 (define @t675 () (= (_ @t671 @t553) (_ @t667 @t553))) % 0.80/1.08 (define @t676 () (@var "Z4" tptp.nat)) % 0.80/1.08 (define @t677 () (_ (_ tptp.ord_less_nat @t676) @t553)) % 0.80/1.08 (define @t678 () (@list @t676)) % 0.80/1.08 (define @t679 () (exists @t678 (forall @t555 (=> @t677 @t675)))) % 0.80/1.08 (define @t680 () (= @t570 (_ @t669 @t553))) % 0.80/1.08 (define @t681 () (exists @t678 (forall @t555 (=> @t677 @t680)))) % 0.80/1.08 (define @t682 () (@list @t344 @t669 @t671 @t667)) % 0.80/1.08 (define @t683 () (= (or @t567 @t672) (or @t670 @t668))) % 0.80/1.08 (define @t684 () (not (= @t455 @t559))) % 0.80/1.08 (define @t685 () (_ @t561 @t559)) % 0.80/1.08 (define @t686 () (_ (_ tptp.ord_less_nat @t559) @t455)) % 0.80/1.08 (define @t687 () (_ @t663 @t676)) % 0.80/1.08 (define @t688 () (exists @t678 (forall @t555 (=> @t687 @t675)))) % 0.80/1.08 (define @t689 () (exists @t678 (forall @t555 (=> @t687 @t680)))) % 0.80/1.08 (define @t690 () (= @t589 @t588)) % 0.80/1.08 (define @t691 () (@list @t588 @t589)) % 0.80/1.08 (define @t692 () (not @t690)) % 0.80/1.08 (define @t693 () (_ tptp.groups1792256535list_a tptp.qs2)) % 0.80/1.08 (define @t694 () (= tptp.a3 @t693)) % 0.80/1.08 (define @t695 () (not @t694)) % 0.80/1.08 (define @t696 () (@var "Ss2" tptp.list_set_a)) % 0.80/1.08 (define @t697 () (lambda (@list @t573 @t696) (_ (_ (_ tptp.bij_betw_list_a_a tptp.groups1792256535list_a) (_ tptp.listset_a @t696)) @t573))) % 0.80/1.08 (define @t698 () (@var "G3" (-> tptp.a tptp.a))) % 0.80/1.08 (define @t699 () (_ @t698 @t362)) % 0.80/1.08 (define @t700 () (@var "F3" (-> tptp.a tptp.a))) % 0.80/1.08 (define @t701 () (_ @t700 @t362)) % 0.80/1.08 (define @t702 () (lambda (@list @t700 @t573 @t571) (exists (@list @t698) (and (forall @t364 (=> @t574 (and (_ (_ tptp.member_a @t701) @t571) (= (_ @t698 @t701) @t362)))) (forall @t364 (=> @t572 (and (_ (_ tptp.member_a @t699) @t573) (= (_ @t700 @t699) @t362)))))))) % 0.80/1.08 (define @t703 () (@var "G3" (-> tptp.a tptp.list_a))) % 0.80/1.08 (define @t704 () (_ @t703 @t362)) % 0.80/1.08 (define @t705 () (@var "F3" (-> tptp.list_a tptp.a))) % 0.80/1.08 (define @t706 () (_ @t705 @t366)) % 0.80/1.08 (define @t707 () (lambda (@list @t705 @t578 @t571) (exists (@list @t703) (and (forall @t368 (=> @t579 (and (_ (_ tptp.member_a @t706) @t571) (= (_ @t703 @t706) @t366)))) (forall @t364 (=> @t572 (and (_ (_ tptp.member_list_a @t704) @t578) (= (_ @t705 @t704) @t362)))))))) % 0.80/1.08 (define @t708 () (@var "G3" (-> tptp.list_a tptp.a))) % 0.80/1.08 (define @t709 () (_ @t708 @t366)) % 0.80/1.08 (define @t710 () (@var "F3" (-> tptp.a tptp.list_a))) % 0.80/1.08 (define @t711 () (_ @t710 @t362)) % 0.80/1.08 (define @t712 () (lambda (@list @t710 @t573 @t576) (exists (@list @t708) (and (forall @t364 (=> @t574 (and (_ (_ tptp.member_list_a @t711) @t576) (= (_ @t708 @t711) @t362)))) (forall @t368 (=> @t577 (and (_ (_ tptp.member_a @t709) @t573) (= (_ @t710 @t709) @t366)))))))) % 0.80/1.08 (define @t713 () (@var "G3" (-> tptp.list_a tptp.list_a))) % 0.80/1.08 (define @t714 () (_ @t713 @t366)) % 0.80/1.08 (define @t715 () (@var "F3" (-> tptp.list_a tptp.list_a))) % 0.80/1.08 (define @t716 () (_ @t715 @t366)) % 0.80/1.08 (define @t717 () (lambda (@list @t715 @t578 @t576) (exists (@list @t713) (and (forall @t368 (=> @t579 (and (_ (_ tptp.member_list_a @t716) @t576) (= (_ @t713 @t716) @t366)))) (forall @t368 (=> @t577 (and (_ (_ tptp.member_list_a @t714) @t578) (= (_ @t715 @t714) @t366)))))))) % 0.80/1.08 (define @t718 () (@var "G3" (-> tptp.nat tptp.nat))) % 0.80/1.08 (define @t719 () (_ @t718 @t359)) % 0.80/1.08 (define @t720 () (_ @t540 @t359)) % 0.80/1.08 (define @t721 () (lambda @t541 (exists (@list @t718) (and (forall @t361 (=> (_ @t360 @t539) (and (_ (_ tptp.member_nat @t720) @t538) (= (_ @t718 @t720) @t359)))) (forall @t361 (=> (_ @t360 @t538) (and (_ (_ tptp.member_nat @t719) @t539) (= (_ @t540 @t719) @t359)))))))) % 0.80/1.08 (define @t722 () (@var "P2" (-> tptp.a Bool))) % 0.80/1.08 (define @t723 () (_ tptp.ord_less_nat @t652)) % 0.80/1.08 (define @t724 () (lambda (@list @t722 @t285) (exists @t653 (and (_ @t723 @t290) (_ @t722 (_ @t286 @t652)))))) % 0.80/1.08 (define @t725 () (@var "P2" (-> tptp.set_a Bool))) % 0.80/1.08 (define @t726 () (lambda (@list @t725 @t292) (exists @t653 (and (_ @t723 @t297) (_ @t725 (_ @t293 @t652)))))) % 0.80/1.08 (define @t727 () (@var "T2" tptp.a)) % 0.80/1.08 (define @t728 () (_ tptp.member_a @t727)) % 0.80/1.08 (define @t729 () (lambda @t575 (forall (@list @t727) (=> (_ @t728 @t573) (_ @t728 @t571))))) % 0.80/1.08 (define @t730 () (@var "T2" tptp.list_a)) % 0.80/1.08 (define @t731 () (_ tptp.member_list_a @t730)) % 0.80/1.08 (define @t732 () (lambda @t580 (forall (@list @t730) (=> (_ @t731 @t578) (_ @t731 @t576))))) % 0.80/1.08 (define @t733 () (@var "Y4" (-> Bool tptp.nat))) % 0.80/1.08 (define @t734 () (@var "X7" (-> Bool tptp.nat))) % 0.80/1.08 (define @t735 () (lambda (@list @t734 @t733) (and (_ (_ tptp.ord_less_eq_nat (_ @t734 false)) (_ @t733 false)) (_ (_ tptp.ord_less_eq_nat (_ @t734 true)) (_ @t733 true))))) % 0.80/1.08 (define @t736 () (lambda @t691 (and @t591 @t692))) % 0.80/1.08 (define @t737 () (tptp.mset_a tptp.qs2)) % 0.80/1.08 (define @t738 () (tptp.mset_a tptp.qs)) % 0.80/1.08 (define @t739 () (tptp.groups1792256535list_a tptp.qs2)) % 0.80/1.08 (define @t740 () (tptp.groups1792256535list_a tptp.qs)) % 0.80/1.08 (define @t741 () (= @t4 @t693)) % 0.80/1.08 (define @t742 () (tptp.mset_a @t67)) % 0.80/1.08 (define @t743 () (tptp.comm_m543484931mset_a @t742)) % 0.80/1.08 (define @t744 () (tptp.groups1792256535list_a @t67)) % 0.80/1.08 (define @t745 () (= @t68 @t81)) % 0.80/1.08 (define @t746 () (tptp.comm_m543484931mset_a @t738)) % 0.80/1.08 (define @t747 () (= @t740 @t746)) % 0.80/1.08 (define @t748 () (not @t747)) % 0.80/1.08 (define @t749 () (= @t739 (tptp.comm_m543484931mset_a @t737))) % 0.80/1.08 (define @t750 () (not @t749)) % 0.80/1.08 (define @t751 () (= @t740 @t739)) % 0.80/1.08 (define @t752 () (= @t738 @t737)) % 0.80/1.08 (define @t753 () (not @t752)) % 0.80/1.08 (define @t754 () (not @t751)) % 0.80/1.08 (define @t755 () (and @t752 @t754 @t749)) % 0.80/1.08 (assume @p1 @t3) % 0.80/1.08 (assume @p2 (_ (_ tptp.member_a tptp.a3) tptp.a2)) % 0.80/1.08 (assume @p3 (= tptp.a3 @t4)) % 0.80/1.08 (assume @p4 (= @t6 @t5)) % 0.80/1.08 (assume @p5 (not (forall @t11 (=> (= tptp.a3 @t10) (not (_ @t9 @t7)))))) % 0.80/1.08 (assume @p6 (_ (_ tptp.member_list_a tptp.qs2) @t12)) % 0.80/1.08 (assume @p7 (forall (@list @t13 @t15 @t14) (=> @t17 (=> (_ (_ tptp.member518144627iset_a @t14) @t16) (_ (_ tptp.member_multiset_a (_ tptp.groups1592617181iset_a @t14)) @t13))))) % 0.80/1.08 (assume @p8 (forall (@list @t18 @t21 @t19) (=> @t24 (=> @t23 (_ (_ tptp.member_nat @t20) @t18))))) % 0.80/1.08 (assume @p9 (forall (@list @t25 @t28 @t26) (=> @t31 (=> @t30 (_ (_ tptp.member_a @t27) @t25))))) % 0.80/1.08 (assume @p10 (forall (@list @t13 @t15 @t34) (=> @t17 (=> (_ @t37 @t13) (not (forall @t36 (=> @t35 (not (= @t34 @t33))))))))) % 0.80/1.08 (assume @p11 (forall (@list @t18 @t21 @t40) (=> @t24 (=> @t44 (not (forall @t42 (=> @t41 (not (= @t40 @t39))))))))) % 0.80/1.08 (assume @p12 (forall (@list @t25 @t28 @t45) (=> @t31 (=> @t48 (not (forall @t11 (=> @t46 (not (= @t45 @t10))))))))) % 0.80/1.08 (assume @p13 (forall (@list @t15 @t13) (=> (forall @t36 (=> @t35 (_ (_ tptp.member_multiset_a @t33) @t13))) (=> (forall (@list @t51) (=> (_ (_ tptp.member_multiset_a @t51) @t13) (exists (@list @t49) (and (_ (_ tptp.member518144627iset_a @t49) @t16) (= @t51 (_ tptp.groups1592617181iset_a @t49)) (forall (@list @t50) (=> (and (_ (_ tptp.member518144627iset_a @t50) @t16) (= @t51 (_ tptp.groups1592617181iset_a @t50))) (= @t50 @t49))))))) @t17)))) % 0.80/1.08 (assume @p14 (forall (@list @t21 @t18) (=> (forall @t42 (=> @t41 (_ (_ tptp.member_nat @t39) @t18))) (=> (forall @t56 (=> @t55 (exists (@list @t52) (and (_ (_ tptp.member_list_nat @t52) @t22) (= @t54 (_ tptp.groups921905271st_nat @t52)) (forall (@list @t53) (=> (and (_ (_ tptp.member_list_nat @t53) @t22) (= @t54 (_ tptp.groups921905271st_nat @t53))) (= @t53 @t52))))))) @t24)))) % 0.80/1.08 (assume @p15 (forall @t60 (=> (forall @t11 (=> @t46 (_ (_ tptp.member_a @t10) @t25))) (=> (forall (@list @t59) (=> (_ (_ tptp.member_a @t59) @t25) (exists (@list @t57) (and (_ (_ tptp.member_list_a @t57) @t29) (= @t59 (_ tptp.groups1792256535list_a @t57)) (forall (@list @t58) (=> (and (_ (_ tptp.member_list_a @t58) @t29) (= @t59 (_ tptp.groups1792256535list_a @t58))) (= @t58 @t57))))))) @t31)))) % 0.80/1.08 (assume @p16 (forall (@list @t18 @t21 @t19 @t61) (=> @t24 (=> @t23 (=> (_ (_ tptp.member_list_nat @t61) @t22) (=> (= @t20 (_ tptp.groups921905271st_nat @t61)) (= @t19 @t61))))))) % 0.80/1.08 (assume @p17 (forall (@list @t25 @t28 @t26 @t62) (=> @t31 (=> @t30 (=> (_ (_ tptp.member_list_a @t62) @t29) (=> (= @t27 (_ tptp.groups1792256535list_a @t62)) (= @t26 @t62))))))) % 0.80/1.08 (assume @p18 (forall @t66 (= (_ tptp.groups921905271st_nat @t65) @t64))) % 0.80/1.08 (assume @p19 (forall @t70 (= (_ tptp.groups1792256535list_a @t69) @t68))) % 0.80/1.08 (assume @p20 (forall @t75 (=> (_ @t74 @t5) (= (_ (_ tptp.nth_a tptp.qs2) @t71) (_ @t73 @t72))))) % 0.80/1.08 (assume @p21 (_ (_ @t76 (_ tptp.set_ord_lessThan_nat @t6)) (_ tptp.set_ord_lessThan_nat @t5))) % 0.80/1.08 (assume @p22 (forall @t66 (= (_ tptp.comm_m1100186507et_nat @t77) @t64))) % 0.80/1.08 (assume @p23 (forall (@list @t78) (= (_ tptp.comm_m324867663list_a (_ tptp.mset_multiset_list_a @t78)) (_ tptp.groups1271887971list_a @t78)))) % 0.80/1.08 (assume @p24 (forall (@list @t79) (= (_ tptp.comm_m2145643721iset_a (_ tptp.mset_multiset_a @t79)) (_ tptp.groups1592617181iset_a @t79)))) % 0.80/1.08 (assume @p25 @t82) % 0.80/1.08 (assume @p26 (forall (@list @t18 @t21) (=> @t24 (= (_ (_ tptp.image_list_nat_nat tptp.groups921905271st_nat) @t22) @t18)))) % 0.80/1.08 (assume @p27 (forall @t84 (=> @t31 @t83))) % 0.80/1.08 (assume @p28 (_ (_ tptp.hilber2037636820comp_a tptp.a2) tptp.ss1)) % 0.80/1.08 (assume @p29 (_ (_ tptp.member_list_a tptp.qs) @t7)) % 0.80/1.08 (assume @p30 (forall @t88 (= (_ tptp.mset_set_a @t87) @t86))) % 0.80/1.08 (assume @p31 (forall @t92 (= (_ tptp.mset_list_a @t91) @t90))) % 0.80/1.08 (assume @p32 (forall @t70 (= (_ tptp.mset_a @t69) @t80))) % 0.80/1.08 (assume @p33 (not (forall (@list @t94) (=> (_ (_ tptp.member_list_a @t94) @t12) (=> (= (_ tptp.size_size_list_a @t94) @t5) (not (forall @t96 (=> (_ @t95 @t5) (= (_ (_ tptp.nth_a @t94) @t93) (_ @t73 (_ tptp.g @t93))))))))))) % 0.80/1.08 (assume @p34 (_ (_ tptp.perm_set_a tptp.ss1) tptp.ss2)) % 0.80/1.08 (assume @p35 (forall (@list @t97) (exists @t99 (= (_ tptp.mset_set_a @t98) @t97)))) % 0.80/1.08 (assume @p36 (forall (@list @t100) (exists @t102 (= (_ tptp.mset_list_a @t101) @t100)))) % 0.80/1.08 (assume @p37 (forall (@list @t103) (exists @t105 (= (_ tptp.mset_a @t104) @t103)))) % 0.80/1.08 (assume @p38 (forall @t111 (=> @t110 @t109))) % 0.80/1.08 (assume @p39 (forall @t118 (=> @t117 @t116))) % 0.80/1.08 (assume @p40 (forall @t125 (=> @t124 @t123))) % 0.80/1.08 (assume @p41 (forall @t131 (=> @t130 @t129))) % 0.80/1.08 (assume @p42 (forall @t137 (=> @t136 @t135))) % 0.80/1.08 (assume @p43 (forall @t143 (=> @t142 @t141))) % 0.80/1.08 (assume @p44 (forall (@list @t145 @t89 @t106) (=> (_ (_ @t152 (_ tptp.set_ord_lessThan_nat @t108)) (_ tptp.set_ord_lessThan_nat @t107)) (=> (forall @t151 (=> @t150 (= @t148 (_ @t147 @t146)))) @t110)))) % 0.80/1.08 (assume @p45 (forall (@list @t145 @t114 @t112) (=> (_ @t157 (_ tptp.set_ord_lessThan_nat @t113)) (=> (forall @t151 (=> @t156 (= @t155 (_ @t153 @t146)))) @t117)))) % 0.80/1.08 (assume @p46 (forall (@list @t145 @t121 @t119) (=> (_ @t162 (_ tptp.set_ord_lessThan_nat @t120)) (=> (forall @t151 (=> @t161 (= @t160 (_ @t158 @t146)))) @t124)))) % 0.80/1.08 (assume @p47 (forall (@list @t145 @t63 @t126) (=> (_ (_ @t152 (_ tptp.set_ord_lessThan_nat @t128)) (_ tptp.set_ord_lessThan_nat @t127)) (=> (forall @t151 (=> @t165 (= @t164 (_ @t163 @t146)))) @t130)))) % 0.80/1.08 (assume @p48 (forall (@list @t145 @t67 @t132) (=> (_ (_ @t152 @t171) @t170) (=> (forall @t151 (=> @t169 (= @t168 (_ @t166 @t146)))) @t136)))) % 0.80/1.08 (assume @p49 (forall (@list @t145 @t85 @t138) (=> (_ @t178 @t176) (=> (forall @t151 (=> @t175 (= @t174 (_ @t172 @t146)))) @t142)))) % 0.80/1.08 (assume @p50 (forall (@list @t112 @t182 @t145 @t181) (=> @t186 (=> (_ (_ @t152 (_ tptp.set_ord_lessThan_nat @t184)) (_ tptp.set_ord_lessThan_nat (_ tptp.size_s469631926list_a @t181))) (=> (forall @t151 (=> @t185 (= (_ (_ tptp.nth_set_set_list_a @t181) @t144) (_ @t183 @t146)))) (not (forall (@list @t180) (=> (_ (_ tptp.member101195155list_a @t180) (_ tptp.listset_set_list_a @t181)) (=> (= (_ tptp.size_s1635937238list_a @t180) @t113) (not (forall @t96 (=> (_ @t95 @t113) (= (_ (_ tptp.nth_set_list_a @t180) @t93) (_ @t153 @t179)))))))))))))) % 0.80/1.08 (assume @p51 (forall (@list @t119 @t189 @t145 @t188) (=> @t193 (=> (_ (_ @t152 (_ tptp.set_ord_lessThan_nat @t191)) (_ tptp.set_ord_lessThan_nat (_ tptp.size_s726512144_set_a @t188))) (=> (forall @t151 (=> @t192 (= (_ (_ tptp.nth_set_set_set_a @t188) @t144) (_ @t190 @t146)))) (not (forall (@list @t187) (=> (_ (_ tptp.member814963949_set_a @t187) (_ tptp.listset_set_set_a @t188)) (=> (= (_ tptp.size_s739728560_set_a @t187) @t120) (not (forall @t96 (=> (_ @t95 @t120) (= (_ (_ tptp.nth_set_set_a @t187) @t93) (_ @t158 @t179)))))))))))))) % 0.80/1.08 (assume @p52 (forall (@list @t126 @t196 @t145 @t195) (=> @t200 (=> (_ (_ @t152 (_ tptp.set_ord_lessThan_nat @t198)) (_ tptp.set_ord_lessThan_nat (_ tptp.size_s577819178et_nat @t195))) (=> (forall @t151 (=> @t199 (= (_ (_ tptp.nth_set_nat @t195) @t144) (_ @t197 @t146)))) (not (forall (@list @t194) (=> (_ (_ tptp.member_list_nat @t194) (_ tptp.listset_nat @t195)) (=> (= (_ tptp.size_size_list_nat @t194) @t127) (not (forall @t96 (=> (_ @t95 @t127) (= (_ (_ tptp.nth_nat @t194) @t93) (_ @t163 @t179)))))))))))))) % 0.80/1.08 (assume @p53 (forall (@list @t106 @t114 @t145 @t202) (=> @t203 (=> (_ @t157 (_ tptp.set_ord_lessThan_nat (_ tptp.size_s1635937238list_a @t202))) (=> (forall @t151 (=> @t156 (= (_ (_ tptp.nth_set_list_a @t202) @t144) (_ @t154 @t146)))) (not (forall (@list @t201) (=> (_ (_ tptp.member_list_list_a @t201) (_ tptp.listset_list_a @t202)) (=> (= (_ tptp.size_s1427607542list_a @t201) @t107) (not (forall @t96 (=> (_ @t95 @t107) (= (_ (_ tptp.nth_list_a @t201) @t93) (_ @t147 @t179)))))))))))))) % 0.80/1.08 (assume @p54 (forall (@list @t138 @t121 @t145 @t205) (=> @t206 (=> (_ @t162 (_ tptp.set_ord_lessThan_nat (_ tptp.size_s739728560_set_a @t205))) (=> (forall @t151 (=> @t161 (= (_ (_ tptp.nth_set_set_a @t205) @t144) (_ @t159 @t146)))) (not (forall (@list @t204) (=> (_ (_ tptp.member_list_set_a @t204) (_ tptp.listset_set_a @t205)) (=> (= (_ tptp.size_size_list_set_a @t204) @t139) (not (forall @t96 (=> (_ @t95 @t139) (= (_ (_ tptp.nth_set_a @t204) @t93) (_ @t172 @t179)))))))))))))) % 0.80/1.08 (assume @p55 (forall (@list @t132 @t85 @t145 @t208) (=> @t210 (=> (_ @t178 (_ tptp.set_ord_lessThan_nat (_ tptp.size_size_list_set_a @t208))) (=> (forall @t151 (=> @t175 (= (_ (_ tptp.nth_set_a @t208) @t144) (_ @t173 @t146)))) (not (forall (@list @t207) (=> (_ (_ tptp.member_list_a @t207) (_ tptp.listset_a @t208)) (=> (= (_ tptp.size_size_list_a @t207) @t133) (not (forall @t96 (=> (_ @t95 @t133) (= (_ (_ tptp.nth_a @t207) @t93) (_ @t166 @t179)))))))))))))) % 0.80/1.08 (assume @p56 (_ (_ @t76 @t214) @t212)) % 0.80/1.08 (assume @p57 (forall @t92 (= (_ tptp.size_s1427607542list_a @t91) @t108))) % 0.80/1.08 (assume @p58 (forall (@list @t114) (= (_ tptp.size_s1635937238list_a (_ tptp.rev_set_list_a @t114)) @t115))) % 0.80/1.08 (assume @p59 (forall (@list @t121) (= (_ tptp.size_s739728560_set_a (_ tptp.rev_set_set_a @t121)) @t122))) % 0.80/1.08 (assume @p60 (forall @t66 (= (_ tptp.size_size_list_nat @t65) @t128))) % 0.80/1.08 (assume @p61 (forall @t70 (= (_ tptp.size_size_list_a @t69) @t134))) % 0.80/1.08 (assume @p62 (forall @t88 (= (_ tptp.size_size_list_set_a @t87) @t140))) % 0.80/1.08 (assume @p63 (forall (@list @t216 @t215) (= (_ (_ tptp.member_set_nat @t216) (_ tptp.set_or1597314339et_nat @t215)) (_ (_ tptp.ord_less_set_nat @t216) @t215)))) % 0.80/1.08 (assume @p64 (forall (@list @t218 @t217) (= (_ (_ tptp.member_set_list_a @t218) (_ tptp.set_or1578766727list_a @t217)) (_ (_ tptp.ord_less_set_list_a @t218) @t217)))) % 0.80/1.08 (assume @p65 (forall (@list @t220 @t219) (= (_ (_ tptp.member_set_a @t220) (_ tptp.set_or1164043265_set_a @t219)) (_ (_ tptp.ord_less_set_a @t220) @t219)))) % 0.80/1.08 (assume @p66 (forall (@list @t71 @t221) (= (_ (_ tptp.member_nat @t71) (_ tptp.set_ord_lessThan_nat @t221)) (_ @t74 @t221)))) % 0.80/1.08 (assume @p67 (forall (@list @t223 @t222) (=> (= (_ tptp.size_s1657263798iset_a @t223) @t227) (=> (forall @t151 (=> (_ @t149 @t227) (_ (_ tptp.member_multiset_a (_ @t226 @t144)) (_ @t225 @t144)))) @t224)))) % 0.80/1.08 (assume @p68 (forall (@list @t229 @t228) (=> (= (_ tptp.size_s575106428list_a @t229) @t233) (=> (forall @t151 (=> (_ @t149 @t233) (_ (_ tptp.member_list_list_a (_ @t232 @t144)) (_ @t231 @t144)))) @t230)))) % 0.80/1.08 (assume @p69 (forall (@list @t235 @t234) (=> (= (_ tptp.size_s341332310_set_a @t235) @t239) (=> (forall @t151 (=> (_ @t149 @t239) (_ (_ tptp.member_list_set_a (_ @t238 @t144)) (_ @t237 @t144)))) @t236)))) % 0.80/1.08 (assume @p70 (forall (@list @t112 @t182) (=> (= @t113 @t184) (=> (forall @t151 (=> @t185 (_ (_ tptp.member_set_list_a @t240) (_ @t183 @t144)))) @t186)))) % 0.80/1.08 (assume @p71 (forall (@list @t119 @t189) (=> (= @t120 @t191) (=> (forall @t151 (=> @t192 (_ (_ tptp.member_set_set_a @t241) (_ @t190 @t144)))) @t193)))) % 0.80/1.08 (assume @p72 (forall (@list @t126 @t196) (=> (= @t127 @t198) (=> (forall @t151 (=> @t199 (_ (_ tptp.member_nat @t242) (_ @t197 @t144)))) @t200)))) % 0.80/1.08 (assume @p73 (forall (@list @t106 @t114) (=> (= @t107 @t115) (=> (forall @t151 (=> @t156 (_ (_ tptp.member_list_a @t243) @t155))) @t203)))) % 0.80/1.08 (assume @p74 (forall @t246 (=> @t245 (=> (forall @t151 (=> @t175 (_ (_ tptp.member_a @t244) @t174))) @t210)))) % 0.80/1.08 (assume @p75 (forall @t249 (=> @t248 (=> (forall @t151 (=> @t161 (_ (_ tptp.member_set_a @t247) @t160))) @t206)))) % 0.80/1.08 (assume @p76 (= @t5 @t213)) % 0.80/1.08 (assume @p77 (_ (_ (_ tptp.bij_betw_nat_nat tptp.f) @t212) @t214)) % 0.80/1.08 (assume @p78 (forall @t111 (=> @t109 (=> (forall @t151 (=> @t150 (= @t148 @t243))) @t250)))) % 0.80/1.08 (assume @p79 (forall @t118 (=> @t116 (=> (forall @t151 (=> @t156 (= @t155 @t240))) @t251)))) % 0.80/1.08 (assume @p80 (forall @t125 (=> @t123 (=> (forall @t151 (=> @t161 (= @t160 @t241))) @t252)))) % 0.80/1.08 (assume @p81 (forall @t131 (=> @t129 (=> (forall @t151 (=> @t165 (= @t164 @t242))) @t253)))) % 0.80/1.08 (assume @p82 (forall @t137 (=> @t135 (=> (forall @t151 (=> @t169 (= @t168 @t244))) @t254)))) % 0.80/1.08 (assume @p83 (forall @t143 (=> @t141 (=> (forall @t151 (=> @t175 (= @t174 @t247))) @t255)))) % 0.80/1.08 (assume @p84 (forall (@list @t221 @t259) (= (forall @t263 (=> @t262 (exists (@list @t265) (_ @t260 @t265)))) (exists (@list @t257) (and (= @t264 @t221) (forall @t263 (=> @t262 (_ @t260 @t258)))))))) % 0.80/1.08 (assume @p85 (forall (@list @t221 @t268) (= (forall @t263 (=> @t262 (exists (@list @t271) (_ @t269 @t271)))) (exists (@list @t266) (and (= @t270 @t221) (forall @t263 (=> @t262 (_ @t269 @t267)))))))) % 0.80/1.08 (assume @p86 (forall (@list @t221 @t274) (= (forall @t263 (=> @t262 (exists (@list @t277) (_ @t275 @t277)))) (exists (@list @t272) (and (= @t276 @t221) (forall @t263 (=> @t262 (_ @t275 @t273)))))))) % 0.80/1.08 (assume @p87 (forall (@list @t221 @t280) (= (forall @t263 (=> @t262 (exists @t284 (_ @t281 @t283)))) (exists (@list @t278) (and (= @t282 @t221) (forall @t263 (=> @t262 (_ @t281 @t279)))))))) % 0.80/1.08 (assume @p88 (forall (@list @t221 @t288) (= (forall @t263 (=> @t262 (exists (@list @t291) (_ @t289 @t291)))) (exists (@list @t285) (and (= @t290 @t221) (forall @t263 (=> @t262 (_ @t289 @t287)))))))) % 0.80/1.08 (assume @p89 (forall (@list @t221 @t295) (= (forall @t263 (=> @t262 (exists (@list @t298) (_ @t296 @t298)))) (exists (@list @t292) (and (= @t297 @t221) (forall @t263 (=> @t262 (_ @t296 @t294)))))))) % 0.80/1.08 (assume @p90 (= (lambda (@list @t301 @t300) (= @t301 @t300)) (lambda (@list @t257 @t299) (and (= @t264 (_ tptp.size_s1427607542list_a @t299)) (forall @t263 (=> (_ @t261 @t264) (= @t258 (_ (_ tptp.nth_list_a @t299) @t256)))))))) % 0.80/1.08 (assume @p91 (= (lambda (@list @t304 @t303) (= @t304 @t303)) (lambda (@list @t266 @t302) (and (= @t270 (_ tptp.size_s1635937238list_a @t302)) (forall @t263 (=> (_ @t261 @t270) (= @t267 (_ (_ tptp.nth_set_list_a @t302) @t256)))))))) % 0.80/1.08 (assume @p92 (= (lambda (@list @t307 @t306) (= @t307 @t306)) (lambda (@list @t272 @t305) (and (= @t276 (_ tptp.size_s739728560_set_a @t305)) (forall @t263 (=> (_ @t261 @t276) (= @t273 (_ (_ tptp.nth_set_set_a @t305) @t256)))))))) % 0.80/1.08 (assume @p93 (= (lambda (@list @t310 @t309) (= @t310 @t309)) (lambda (@list @t278 @t308) (and (= @t282 (_ tptp.size_size_list_nat @t308)) (forall @t263 (=> (_ @t261 @t282) (= @t279 (_ (_ tptp.nth_nat @t308) @t256)))))))) % 0.80/1.08 (assume @p94 (= (lambda (@list @t313 @t312) (= @t313 @t312)) (lambda (@list @t285 @t311) (and (= @t290 (_ tptp.size_size_list_a @t311)) (forall @t263 (=> (_ @t261 @t290) (= @t287 (_ (_ tptp.nth_a @t311) @t256)))))))) % 0.80/1.08 (assume @p95 (= (lambda (@list @t316 @t315) (= @t316 @t315)) (lambda (@list @t292 @t314) (and (= @t297 (_ tptp.size_size_list_set_a @t314)) (forall @t263 (=> (_ @t261 @t297) (= @t294 (_ (_ tptp.nth_set_a @t314) @t256)))))))) % 0.80/1.08 (assume @p96 (forall @t322 (= (= @t321 @t320) @t319))) % 0.80/1.08 (assume @p97 (forall @t137 (= (= @t69 @t323) @t254))) % 0.80/1.08 (assume @p98 (forall @t143 (= (= @t87 @t324) @t255))) % 0.80/1.08 (assume @p99 (forall @t70 (= (_ tptp.rev_a @t69) @t67))) % 0.80/1.08 (assume @p100 (forall @t88 (= (_ tptp.rev_set_a @t87) @t85))) % 0.80/1.08 (assume @p101 (= @t213 @t211)) % 0.80/1.08 (assume @p102 (forall @t75 (=> @t327 (= (_ @t326 @t71) (_ @t325 @t72))))) % 0.80/1.08 (assume @p103 (forall @t75 (=> @t329 (= (_ @t325 @t71) (_ @t326 @t328))))) % 0.80/1.08 (assume @p104 (not (forall @t334 (=> (_ (_ @t333 @t212) @t214) (not (forall @t96 (=> (_ @t95 @t211) @t332))))))) % 0.80/1.08 (assume @p105 (exists @t334 (and (_ (_ @t333 @t214) @t212) (forall @t96 (=> (_ @t95 @t213) @t332))))) % 0.80/1.08 (assume @p106 (forall @t75 (=> @t327 (= (_ tptp.f @t72) @t71)))) % 0.80/1.08 (assume @p107 (forall @t75 (=> @t329 (= (_ tptp.g @t328) @t71)))) % 0.80/1.08 (assume @p108 (forall (@list @t119 @t189 @t71) (=> @t193 (=> (_ @t74 @t191) (_ (_ tptp.member_set_set_a (_ @t158 @t71)) (_ @t190 @t71)))))) % 0.80/1.08 (assume @p109 (forall (@list @t112 @t182 @t71) (=> @t186 (=> (_ @t74 @t184) (_ (_ tptp.member_set_list_a (_ @t153 @t71)) (_ @t183 @t71)))))) % 0.80/1.08 (assume @p110 (forall (@list @t223 @t222 @t71) (=> @t224 (=> (_ @t74 @t227) (_ (_ tptp.member_multiset_a (_ @t226 @t71)) (_ @t225 @t71)))))) % 0.80/1.08 (assume @p111 (forall (@list @t229 @t228 @t71) (=> @t230 (=> (_ @t74 @t233) (_ (_ tptp.member_list_list_a (_ @t232 @t71)) (_ @t231 @t71)))))) % 0.80/1.08 (assume @p112 (forall (@list @t235 @t234 @t71) (=> @t236 (=> (_ @t74 @t239) (_ (_ tptp.member_list_set_a (_ @t238 @t71)) (_ @t237 @t71)))))) % 0.80/1.08 (assume @p113 (forall (@list @t126 @t196 @t71) (=> @t200 (=> (_ @t74 @t198) (_ (_ tptp.member_nat (_ @t163 @t71)) (_ @t197 @t71)))))) % 0.80/1.08 (assume @p114 (forall (@list @t138 @t121 @t71) (=> @t206 (=> (_ @t74 @t122) (_ (_ tptp.member_set_a (_ @t172 @t71)) (_ @t159 @t71)))))) % 0.80/1.08 (assume @p115 (forall (@list @t106 @t114 @t71) (=> @t203 (=> (_ @t74 @t115) (_ (_ tptp.member_list_a (_ @t147 @t71)) (_ @t154 @t71)))))) % 0.80/1.08 (assume @p116 (forall (@list @t132 @t85 @t71) (=> @t210 (=> @t336 (_ (_ tptp.member_a (_ @t166 @t71)) @t335))))) % 0.80/1.08 (assume @p117 (forall @t111 (=> (not @t109) (not @t250)))) % 0.80/1.08 (assume @p118 (forall @t118 (=> (not @t116) (not @t251)))) % 0.80/1.08 (assume @p119 (forall @t125 (=> (not @t123) (not @t252)))) % 0.80/1.08 (assume @p120 (forall @t131 (=> (not @t129) (not @t253)))) % 0.80/1.08 (assume @p121 (forall @t137 (=> (not @t135) (not @t254)))) % 0.80/1.08 (assume @p122 (forall @t143 (=> (not @t141) (not @t255)))) % 0.80/1.08 (assume @p123 (forall (@list @t34 @t337) (= (_ @t37 (_ tptp.collect_multiset_a @t337)) (_ @t337 @t34)))) % 0.80/1.08 (assume @p124 (forall (@list @t338 @t339) (= (_ (_ tptp.member_list_list_a @t338) (_ tptp.collect_list_list_a @t339)) (_ @t339 @t338)))) % 0.80/1.08 (assume @p125 (forall (@list @t340 @t341) (= (_ (_ tptp.member_list_set_a @t340) (_ tptp.collect_list_set_a @t341)) (_ @t341 @t340)))) % 0.80/1.08 (assume @p126 (forall (@list @t342 @t343) (= (_ (_ tptp.member_set_a @t342) (_ tptp.collect_set_a @t343)) (_ @t343 @t342)))) % 0.80/1.08 (assume @p127 (forall (@list @t40 @t344) (= (_ @t43 (_ tptp.collect_nat @t344)) @t345))) % 0.80/1.08 (assume @p128 (forall (@list @t45 @t346) (= (_ @t47 @t347) (_ @t346 @t45)))) % 0.80/1.08 (assume @p129 (forall (@list @t348 @t349) (= (_ @t351 @t350) (_ @t349 @t348)))) % 0.80/1.08 (assume @p130 (forall (@list @t13) (= (_ tptp.collect_multiset_a (lambda (@list @t352) (_ (_ tptp.member_multiset_a @t352) @t13))) @t13))) % 0.80/1.08 (assume @p131 (forall (@list @t353) (= (_ tptp.collect_list_list_a (lambda (@list @t354) (_ (_ tptp.member_list_list_a @t354) @t353))) @t353))) % 0.80/1.08 (assume @p132 (forall (@list @t355) (= (_ tptp.collect_list_set_a (lambda (@list @t356) (_ (_ tptp.member_list_set_a @t356) @t355))) @t355))) % 0.80/1.08 (assume @p133 (forall (@list @t357) (= (_ tptp.collect_set_a (lambda (@list @t358) (_ (_ tptp.member_set_a @t358) @t357))) @t357))) % 0.80/1.08 (assume @p134 (forall (@list @t18) (= (_ tptp.collect_nat (lambda @t361 (_ @t360 @t18))) @t18))) % 0.80/1.08 (assume @p135 (forall (@list @t25) (= (_ tptp.collect_a (lambda @t364 (_ @t363 @t25))) @t25))) % 0.80/1.08 (assume @p136 (forall (@list @t365) (= (_ tptp.collect_list_a (lambda @t368 (_ @t367 @t365))) @t365))) % 0.80/1.08 (assume @p137 (forall (@list @t349 @t369) (=> (forall @t372 (= @t371 (_ @t369 @t370))) (= @t350 (_ tptp.collect_list_a @t369))))) % 0.80/1.08 (assume @p138 (forall (@list @t346 @t373) (=> (forall @t375 (= (_ @t346 @t374) (_ @t373 @t374))) (= @t347 (_ tptp.collect_a @t373))))) % 0.80/1.08 (assume @p139 (forall @t377 (exists @t102 (= (_ tptp.size_s1427607542list_a @t101) @t376)))) % 0.80/1.08 (assume @p140 (forall @t377 (exists @t380 (= @t379 @t376)))) % 0.80/1.08 (assume @p141 (forall @t377 (exists @t383 (= @t382 @t376)))) % 0.80/1.08 (assume @p142 (forall @t377 (exists @t386 (= @t385 @t376)))) % 0.80/1.08 (assume @p143 (forall @t377 (exists @t105 (= @t387 @t376)))) % 0.80/1.08 (assume @p144 (forall @t377 (exists @t99 (= @t388 @t376)))) % 0.80/1.08 (assume @p145 (forall @t137 (= (= @t69 @t132) (= @t67 @t323)))) % 0.80/1.08 (assume @p146 (forall @t143 (= (= @t87 @t138) (= @t85 @t324)))) % 0.80/1.08 (assume @p147 (forall (@list @t389 @t376) (= (_ (_ tptp.ord_less_set_nat (_ tptp.set_ord_lessThan_nat @t389)) (_ tptp.set_ord_lessThan_nat @t376)) (_ (_ tptp.ord_less_nat @t389) @t376)))) % 0.80/1.08 (assume @p148 (forall (@list @t390 @t114) (=> (forall @t380 (=> (forall (@list @t391) (=> (_ (_ tptp.ord_less_nat (_ tptp.size_s1635937238list_a @t391)) @t379) (_ @t390 @t391))) (_ @t390 @t378))) (_ @t390 @t114)))) % 0.80/1.08 (assume @p149 (forall (@list @t392 @t121) (=> (forall @t383 (=> (forall (@list @t393) (=> (_ (_ tptp.ord_less_nat (_ tptp.size_s739728560_set_a @t393)) @t382) (_ @t392 @t393))) (_ @t392 @t381))) (_ @t392 @t121)))) % 0.80/1.08 (assume @p150 (forall (@list @t394 @t63) (=> (forall @t386 (=> (forall (@list @t395) (=> (_ (_ tptp.ord_less_nat (_ tptp.size_size_list_nat @t395)) @t385) (_ @t394 @t395))) (_ @t394 @t384))) (_ @t394 @t63)))) % 0.80/1.08 (assume @p151 (forall (@list @t349 @t67) (=> (forall @t105 (=> (forall (@list @t396) (=> (_ (_ tptp.ord_less_nat (_ tptp.size_size_list_a @t396)) @t387) (_ @t349 @t396))) (_ @t349 @t104))) (_ @t349 @t67)))) % 0.80/1.08 (assume @p152 (forall (@list @t341 @t85) (=> (forall @t99 (=> (forall (@list @t397) (=> (_ (_ tptp.ord_less_nat (_ tptp.size_size_list_set_a @t397)) @t388) (_ @t341 @t397))) (_ @t341 @t98))) (_ @t341 @t85)))) % 0.80/1.08 (assume @p153 (forall @t246 (=> @t210 @t245))) % 0.80/1.08 (assume @p154 (forall @t249 (=> @t206 @t248))) % 0.80/1.08 (assume @p155 (forall @t137 (=> @t398 (exists @t334 (and (_ (_ @t333 @t171) @t170) (forall @t96 (=> (_ @t95 @t134) (= (_ @t167 @t93) (_ @t166 @t331))))))))) % 0.80/1.08 (assume @p156 (forall @t143 (=> @t400 (exists @t334 (and (_ (_ @t333 @t177) @t176) (forall @t96 (=> (_ @t95 @t140) (= (_ @t173 @t93) (_ @t172 @t331))))))))) % 0.80/1.08 (assume @p157 (= tptp.g (_ (_ tptp.hilber815131374at_nat @t212) tptp.f))) % 0.80/1.08 (assume @p158 (forall (@list @t401) (_ (_ tptp.perm_set_a @t401) @t401))) % 0.80/1.08 (assume @p159 (forall (@list @t404 @t402 @t407 @t25) (=> @t411 (=> @t409 @t406)))) % 0.80/1.08 (assume @p160 (forall (@list @t414 @t412 @t407 @t25) (=> @t418 (=> @t409 @t416)))) % 0.80/1.08 (assume @p161 (forall (@list @t404 @t419 @t422 @t365) (=> @t426 (=> @t424 @t421)))) % 0.80/1.08 (assume @p162 (forall (@list @t414 @t427 @t422 @t365) (=> @t431 (=> @t424 @t429)))) % 0.80/1.08 (assume @p163 (forall @t137 (= @t136 @t398))) % 0.80/1.08 (assume @p164 (forall @t143 (= @t142 @t400))) % 0.80/1.08 (assume @p165 (forall @t88 (_ (_ tptp.perm_set_a @t87) @t85))) % 0.80/1.08 (assume @p166 (forall @t137 (=> @t398 @t135))) % 0.80/1.08 (assume @p167 (forall @t143 (=> @t400 @t141))) % 0.80/1.08 (assume @p168 (forall @t438 (=> @t437 @t435))) % 0.80/1.08 (assume @p169 (forall (@list @t422 @t365 @t439) (=> @t424 (=> (_ (_ tptp.ord_less_nat @t440) (_ tptp.size_size_list_a @t439)) (not (= @t422 @t439)))))) % 0.80/1.08 (assume @p170 (forall (@list @t442 @t355 @t441) (=> @t444 (=> (_ (_ tptp.ord_less_nat @t443) (_ tptp.size_size_list_set_a @t441)) (not (= @t442 @t441)))))) % 0.80/1.08 (assume @p171 (forall @t70 (= (_ tptp.size_size_multiset_a @t80) @t134))) % 0.80/1.08 (assume @p172 (forall @t88 (= (_ tptp.size_s657334288_set_a @t86) @t140))) % 0.80/1.08 (assume @p173 (forall @t449 (=> (_ (_ tptp.ord_less_set_a @t25) @t445) @t448))) % 0.80/1.08 (assume @p174 (forall @t454 (=> (_ (_ tptp.ord_less_set_list_a @t365) @t450) @t453))) % 0.80/1.08 (assume @p175 (forall (@list @t407 @t25 @t402) (=> @t409 (_ (_ tptp.member_a @t410) @t403)))) % 0.80/1.08 (assume @p176 (forall (@list @t407 @t25 @t412) (=> @t409 (_ (_ tptp.member_list_a @t417) @t413)))) % 0.80/1.08 (assume @p177 (forall (@list @t422 @t365 @t419) (=> @t424 (_ (_ tptp.member_a @t425) @t420)))) % 0.80/1.08 (assume @p178 (forall (@list @t422 @t365 @t427) (=> @t424 (_ (_ tptp.member_list_a @t430) @t428)))) % 0.80/1.08 (assume @p179 (forall (@list @t407 @t25 @t404 @t402) (=> @t409 (=> @t411 @t406)))) % 0.80/1.08 (assume @p180 (forall (@list @t407 @t25 @t414 @t412) (=> @t409 (=> @t418 @t416)))) % 0.80/1.08 (assume @p181 (forall (@list @t422 @t365 @t404 @t419) (=> @t424 (=> @t426 @t421)))) % 0.80/1.08 (assume @p182 (forall (@list @t422 @t365 @t414 @t427) (=> @t424 (=> @t431 @t429)))) % 0.80/1.08 (assume @p183 (forall @t438 (=> @t437 (forall @t456 (=> (_ (_ tptp.member_nat @t455) @t18) (_ (_ tptp.member_nat (_ @t145 @t455)) @t432)))))) % 0.80/1.08 (assume @p184 (forall @t438 (=> @t437 (exists (@list @t457) (_ (_ (_ tptp.bij_betw_nat_nat @t457) @t432) @t18))))) % 0.80/1.08 (assume @p185 (forall (@list @t18 @t145 @t459 @t458) (=> (forall @t56 (=> @t55 (= (_ @t145 @t54) (_ @t459 @t54)))) (= @t460 (_ (_ (_ tptp.bij_betw_nat_nat @t459) @t18) @t458))))) % 0.80/1.08 (assume @p186 (forall (@list @t402 @t25 @t445 @t45) (=> (_ (_ (_ tptp.bij_betw_a_a @t402) @t25) @t445) (=> @t48 (_ @t461 @t445))))) % 0.80/1.08 (assume @p187 (forall (@list @t412 @t25 @t450 @t45) (=> (_ (_ (_ tptp.bij_betw_a_list_a @t412) @t25) @t450) (=> @t48 (_ @t462 @t450))))) % 0.80/1.08 (assume @p188 (forall (@list @t419 @t365 @t445 @t348) (=> (_ (_ (_ tptp.bij_betw_list_a_a @t419) @t365) @t445) (=> @t464 (_ @t463 @t445))))) % 0.80/1.08 (assume @p189 (forall (@list @t427 @t365 @t450 @t348) (=> (_ (_ (_ tptp.bij_be94573046list_a @t427) @t365) @t450) (=> @t464 (_ @t465 @t450))))) % 0.80/1.08 (assume @p190 (forall (@list @t145 @t18 @t432 @t40) (=> @t437 (=> @t44 (_ (_ tptp.member_nat @t466) @t432))))) % 0.80/1.08 (assume @p191 (forall @t143 (=> @t400 (_ @t467 @t85)))) % 0.80/1.08 (assume @p192 (forall (@list @t85 @t138 @t468) (=> @t400 (=> (_ @t467 @t468) (_ @t399 @t468))))) % 0.80/1.08 (assume @p193 (forall (@list @t145 @t18 @t458 @t469) (=> @t460 (=> (_ (_ tptp.member_nat @t469) @t458) (= (_ @t145 (_ @t470 @t469)) @t469))))) % 0.80/1.08 (assume @p194 (forall @t471 (=> @t460 (=> @t44 (= (_ @t470 @t466) @t40))))) % 0.80/1.08 (assume @p195 (forall @t471 (=> @t460 (=> @t44 (= (_ (_ (_ tptp.hilber815131374at_nat @t458) @t470) @t40) @t466))))) % 0.80/1.08 (assume @p196 (forall @t438 (=> @t437 (_ (_ @t472 @t432) @t18)))) % 0.80/1.08 (assume @p197 (forall (@list @t18 @t145 @t318 @t317) (=> (= @t477 @t476) (=> @t475 (=> @t473 @t319))))) % 0.80/1.08 (assume @p198 (forall (@list @t407 @t402 @t25) (=> (_ @t408 @t403) (_ (_ tptp.member_a (_ (_ (_ tptp.hilbert_inv_into_a_a @t25) @t402) @t407)) @t25)))) % 0.80/1.08 (assume @p199 (forall (@list @t407 @t419 @t365) (=> (_ @t408 @t420) (_ (_ tptp.member_list_a (_ (_ (_ tptp.hilber2125729734st_a_a @t365) @t419) @t407)) @t365)))) % 0.80/1.08 (assume @p200 (forall (@list @t422 @t412 @t25) (=> (_ @t423 @t413) (_ (_ tptp.member_a (_ (_ (_ tptp.hilber165648082list_a @t25) @t412) @t422)) @t25)))) % 0.80/1.08 (assume @p201 (forall (@list @t422 @t427 @t365) (=> (_ @t423 @t428) (_ (_ tptp.member_list_a (_ (_ (_ tptp.hilber921249868list_a @t365) @t427) @t422)) @t365)))) % 0.80/1.08 (assume @p202 (forall (@list @t318 @t145 @t18) (=> @t475 (_ (_ tptp.member_nat @t477) @t18)))) % 0.80/1.08 (assume @p203 (forall (@list @t317 @t145 @t18) (=> @t473 (= (_ @t145 @t476) @t317)))) % 0.80/1.08 (assume @p204 (forall @t60 (=> @t478 (=> @t83 @t31)))) % 0.80/1.08 (assume @p205 (forall (@list @t221 @t479) (=> (_ (_ tptp.ord_less_nat @t221) (_ tptp.size_size_list_nat @t479)) (_ (_ tptp.ord_less_eq_nat (_ (_ tptp.nth_nat @t479) @t221)) (_ tptp.groups921905271st_nat @t479))))) % 0.80/1.08 (assume @p206 (forall (@list @t71 @t67 @t481) (=> @t485 (=> (_ @t484 @t134) (_ (_ tptp.perm_a (_ (_ (_ tptp.list_update_a (_ @t483 @t482)) @t481) @t480)) @t67))))) % 0.80/1.08 (assume @p207 (forall (@list @t71 @t85 @t481) (=> @t336 (=> (_ @t484 @t140) (_ (_ tptp.perm_set_a (_ (_ (_ tptp.list_update_set_a (_ @t487 @t486)) @t481) @t335)) @t85))))) % 0.80/1.08 (assume @p208 (forall (@list @t71 @t488 @t481) (=> @t493 (=> (_ @t484 @t492) (= (_ tptp.mset_a (_ (_ (_ tptp.list_update_a (_ (_ (_ tptp.list_update_a @t488) @t481) @t491)) @t71) (_ @t490 @t481))) @t489))))) % 0.80/1.08 (assume @p209 (forall (@list @t71 @t494 @t481) (=> @t499 (=> (_ @t484 @t498) (= (_ tptp.mset_set_a (_ (_ (_ tptp.list_update_set_a (_ (_ (_ tptp.list_update_set_a @t494) @t481) @t497)) @t71) (_ @t496 @t481))) @t495))))) % 0.80/1.08 (assume @p210 (forall (@list @t71 @t500) (=> (_ @t74 (_ tptp.size_s1427607542list_a @t500)) (_ (_ tptp.member_list_a (_ (_ tptp.nth_list_a @t500) @t71)) (_ tptp.set_mset_list_a (_ tptp.mset_list_a @t500)))))) % 0.80/1.08 (assume @p211 (forall (@list @t71 @t488) (=> @t493 (_ (_ tptp.member_a @t491) (_ tptp.set_mset_a @t489))))) % 0.80/1.08 (assume @p212 (forall (@list @t71 @t494) (=> @t499 (_ (_ tptp.member_set_a @t497) (_ tptp.set_mset_set_a @t495))))) % 0.80/1.08 (assume @p213 (forall (@list @t407 @t502) (= (_ @t408 (_ tptp.set_mset_a (_ tptp.comm_m2145643721iset_a @t502))) (exists (@list @t501) (and (_ (_ tptp.member_multiset_a @t501) (_ tptp.set_mset_multiset_a @t502)) (_ @t408 (_ tptp.set_mset_a @t501))))))) % 0.80/1.08 (assume @p214 (forall (@list @t422 @t504) (= (_ @t423 (_ tptp.set_mset_list_a (_ tptp.comm_m324867663list_a @t504))) (exists (@list @t503) (and (_ (_ tptp.member528267379list_a @t503) (_ tptp.set_ms1660427399list_a @t504)) (_ @t423 (_ tptp.set_mset_list_a @t503))))))) % 0.80/1.08 (assume @p215 (forall @t322 (= (_ (_ tptp.ord_less_eq_set_nat @t321) @t320) @t506))) % 0.80/1.08 (assume @p216 (forall @t509 (=> (_ (_ tptp.ord_less_eq_nat @t134) @t71) @t508))) % 0.80/1.08 (assume @p217 (forall @t513 (=> (_ (_ tptp.ord_less_eq_nat @t140) @t71) @t512))) % 0.80/1.08 (assume @p218 (forall @t509 (= (_ tptp.size_size_list_a @t507) @t134))) % 0.80/1.08 (assume @p219 (forall @t513 (= (_ tptp.size_size_list_set_a @t511) @t140))) % 0.80/1.08 (assume @p220 (forall (@list @t145 @t18 @t318) (=> @t516 (=> @t515 (= (_ @t470 @t514) @t318))))) % 0.80/1.08 (assume @p221 (forall (@list @t67 @t71) (= (_ @t483 @t480) @t67))) % 0.80/1.08 (assume @p222 (forall (@list @t85 @t71) (= (_ @t487 @t335) @t85))) % 0.80/1.08 (assume @p223 (forall (@list @t71 @t481 @t67 @t407) @t521)) % 0.80/1.08 (assume @p224 (forall (@list @t71 @t481 @t85 @t510) @t524)) % 0.80/1.08 (assume @p225 (forall (@list @t145 @t18 @t525) (=> @t516 (=> (_ (_ tptp.ord_less_eq_set_nat @t525) @t18) (= (_ @t526 (_ @t433 @t525)) @t525))))) % 0.80/1.08 (assume @p226 (forall @t527 (=> @t485 (= (_ @t517 @t71) @t407)))) % 0.80/1.08 (assume @p227 (forall @t528 (=> @t336 (= (_ @t522 @t71) @t510)))) % 0.80/1.08 (assume @p228 (forall (@list @t432 @t145 @t18) (=> (_ @t529 @t434) (_ (_ tptp.inj_on_nat_nat @t470) @t432)))) % 0.80/1.08 (assume @p229 (forall (@list @t402 @t445 @t45 @t25) (=> (_ (_ tptp.inj_on_a_a @t402) @t445) (=> @t531 (=> @t530 (= (_ @t461 @t403) @t48)))))) % 0.80/1.08 (assume @p230 (forall (@list @t412 @t445 @t45 @t25) (=> (_ (_ tptp.inj_on_a_list_a @t412) @t445) (=> @t531 (=> @t530 (= (_ @t462 @t413) @t48)))))) % 0.80/1.08 (assume @p231 (forall (@list @t419 @t450 @t348 @t365) (=> (_ (_ tptp.inj_on_list_a_a @t419) @t450) (=> @t533 (=> @t532 (= (_ @t463 @t420) @t464)))))) % 0.80/1.08 (assume @p232 (forall (@list @t427 @t450 @t348 @t365) (=> (_ (_ tptp.inj_on_list_a_list_a @t427) @t450) (=> @t533 (=> @t532 (= (_ @t465 @t428) @t464)))))) % 0.80/1.08 (assume @p233 (forall @t438 (=> @t437 @t516))) % 0.80/1.08 (assume @p234 (forall (@list @t145 @t18 @t318 @t317) (=> @t516 (=> @t515 (=> (= @t514 @t317) (= @t476 @t318)))))) % 0.80/1.08 (assume @p235 (forall (@list @t25 @t402 @t445) (=> (forall @t375 (=> @t535 (_ (_ tptp.member_a (_ @t402 @t374)) @t445))) (_ (_ tptp.ord_less_eq_set_a @t403) @t445)))) % 0.80/1.08 (assume @p236 (forall (@list @t25 @t412 @t450) (=> (forall @t375 (=> @t535 (_ (_ tptp.member_list_a (_ @t412 @t374)) @t450))) (_ (_ tptp.ord_le1301786372list_a @t413) @t450)))) % 0.80/1.08 (assume @p237 (forall (@list @t365 @t419 @t445) (=> (forall @t372 (=> @t537 (_ (_ tptp.member_a (_ @t419 @t370)) @t445))) (_ (_ tptp.ord_less_eq_set_a @t420) @t445)))) % 0.80/1.08 (assume @p238 (forall (@list @t365 @t427 @t450) (=> (forall @t372 (=> @t537 (_ (_ tptp.member_list_a (_ @t427 @t370)) @t450))) (_ (_ tptp.ord_le1301786372list_a @t428) @t450)))) % 0.80/1.08 (assume @p239 (= tptp.bij_betw_nat_nat (lambda @t541 (and (_ (_ tptp.inj_on_nat_nat @t540) @t539) (= (_ (_ tptp.image_nat_nat @t540) @t539) @t538))))) % 0.80/1.08 (assume @p240 (forall @t438 (=> @t516 (=> @t435 @t437)))) % 0.80/1.08 (assume @p241 (forall (@list @t145 @t18) (=> @t516 (_ @t436 @t434)))) % 0.80/1.08 (assume @p242 (forall (@list @t422 @t365 @t349) (=> @t424 (=> (_ @t349 @t422) (exists @t372 (and @t537 (_ (_ tptp.ord_less_eq_nat @t543) @t440) @t371 (forall (@list @t542) (=> (_ (_ tptp.member_list_a @t542) @t365) (=> (_ (_ tptp.ord_less_nat (_ tptp.size_size_list_a @t542)) @t543) (not (_ @t349 @t542))))))))))) % 0.80/1.08 (assume @p243 (forall (@list @t442 @t355 @t341) (=> @t444 (=> (_ @t341 @t442) (exists (@list @t545) (and (_ (_ tptp.member_list_set_a @t545) @t355) (_ (_ tptp.ord_less_eq_nat @t546) @t443) (_ @t341 @t545) (forall (@list @t544) (=> (_ (_ tptp.member_list_set_a @t544) @t355) (=> (_ (_ tptp.ord_less_nat (_ tptp.size_size_list_set_a @t544)) @t546) (not (_ @t341 @t544))))))))))) % 0.80/1.08 (assume @p244 (forall @t550 (=> @t460 (=> @t549 (=> @t548 (_ (_ @t152 @t432) @t547)))))) % 0.80/1.08 (assume @p245 (forall (@list @t18 @t551 @t145 @t458) (=> (forall @t555 (=> (_ @t554 @t18) (= (_ @t551 @t556) @t553))) (=> (forall @t555 (=> (_ @t554 @t458) (= (_ @t145 (_ @t551 @t553)) @t553))) (=> (_ @t552 @t458) (=> (_ (_ tptp.ord_less_eq_set_nat (_ (_ tptp.image_nat_nat @t551) @t458)) @t18) @t460)))))) % 0.80/1.08 (assume @p246 (forall (@list @t145 @t18 @t458 @t547) (=> (= @t434 @t458) (=> (_ (_ tptp.ord_less_eq_set_nat @t547) @t458) (= (_ @t433 (_ @t526 @t547)) @t547))))) % 0.80/1.08 (assume @p247 (forall @t143 (=> @t141 (=> (forall @t151 (=> (_ @t149 @t139) (_ (_ tptp.ord_less_eq_set_a @t174) @t247))) (_ (_ tptp.ord_le1301786372list_a @t209) (_ tptp.listset_a @t138)))))) % 0.80/1.08 (assume @p248 (forall (@list @t71 @t67 @t481 @t407) (=> @t485 (and (=> @t519 (= @t518 @t407)) @t521)))) % 0.80/1.08 (assume @p249 (forall (@list @t71 @t85 @t481 @t510) (=> @t336 (and (=> @t519 (= @t523 @t510)) @t524)))) % 0.80/1.08 (assume @p250 (forall @t527 (=> @t485 (= @t508 (= @t480 @t407))))) % 0.80/1.08 (assume @p251 (forall @t528 (=> @t336 (= @t512 (= @t335 @t510))))) % 0.80/1.08 (assume @p252 (forall @t550 (=> @t460 (=> @t549 (=> @t548 (_ (_ @t472 @t547) @t432)))))) % 0.80/1.08 (assume @p253 (forall @t84 (=> @t31 @t478))) % 0.80/1.08 (assume @p254 (forall (@list @t145 @t18 @t432 @t459) (=> @t516 (=> (_ @t552 @t432) (=> (_ (_ tptp.inj_on_nat_nat @t459) @t432) (=> (_ (_ tptp.ord_less_eq_set_nat (_ (_ tptp.image_nat_nat @t459) @t432)) @t18) (exists (@list @t557) (_ (_ (_ tptp.bij_betw_nat_nat @t557) @t18) @t432)))))))) % 0.80/1.08 (assume @p255 (forall @t558 (_ @t505 @t318))) % 0.80/1.08 (assume @p256 (forall @t564 (exists @t563 (forall @t456 (=> @t562 (not (_ (_ tptp.ord_less_eq_nat @t559) @t455))))))) % 0.80/1.08 (assume @p257 (forall @t564 (exists @t563 (forall @t456 (=> @t562 (_ @t565 @t559)))))) % 0.80/1.08 (assume @p258 (forall (@list @t25 @t445) (=> (forall @t375 (=> @t535 (_ @t534 @t445))) @t530))) % 0.80/1.08 (assume @p259 (forall (@list @t365 @t450) (=> (forall @t372 (=> @t537 (_ @t536 @t450))) @t532))) % 0.80/1.08 (assume @p260 (forall (@list @t344 @t318 @t568) (=> (_ @t344 @t318) (=> (forall @t555 (=> @t570 (_ @t569 @t568))) (not (forall (@list @t566) (=> (_ @t344 @t566) (not (forall @t456 (=> @t567 (_ @t565 @t566))))))))))) % 0.80/1.08 (assume @p261 (= tptp.ord_less_eq_set_a (lambda @t575 (forall @t364 (=> @t574 @t572))))) % 0.80/1.08 (assume @p262 (= tptp.ord_le1301786372list_a (lambda @t580 (forall @t368 (=> @t579 @t577))))) % 0.80/1.08 (assume @p263 (forall @t449 (=> @t530 @t448))) % 0.80/1.08 (assume @p264 (forall @t454 (=> @t532 @t453))) % 0.80/1.08 (assume @p265 (forall (@list @t25 @t445 @t407) (=> @t530 (=> @t409 (_ @t408 @t445))))) % 0.80/1.08 (assume @p266 (forall (@list @t365 @t450 @t422) (=> @t532 (=> @t424 (_ @t423 @t450))))) % 0.80/1.08 (assume @p267 (forall @t587 (=> @t586 (=> @t584 @t582)))) % 0.80/1.08 (assume @p268 (= @t595 (lambda @t592 (and @t591 @t590)))) % 0.80/1.08 (assume @p269 (forall @t599 (=> @t586 (=> @t598 (_ @t597 @t40))))) % 0.80/1.08 (assume @p270 (forall @t605 (=> (forall @t603 (=> (_ (_ tptp.ord_less_eq_nat @t54) @t600) @t602)) @t604))) % 0.80/1.08 (assume @p271 (forall @t606 (_ @t583 @t40))) % 0.80/1.08 (assume @p272 (forall @t611 (=> @t506 (=> @t610 @t608)))) % 0.80/1.08 (assume @p273 (forall @t612 (=> @t584 (=> @t586 @t582)))) % 0.80/1.08 (assume @p274 (forall @t615 (=> @t584 (=> @t614 @t613)))) % 0.80/1.08 (assume @p275 (forall @t615 (=> @t582 @t617))) % 0.80/1.08 (assume @p276 (= @t595 (lambda @t592 (and @t590 @t591)))) % 0.80/1.08 (assume @p277 (forall @t619 (=> @t618 (= @t506 @t319)))) % 0.80/1.08 (assume @p278 (forall @t611 (=> (=> @t506 (not @t610)) (=> (=> @t618 (not @t608)) (=> (=> @t608 (not @t623)) (=> (=> @t623 (not @t618)) (=> (=> @t610 (not @t622)) (not (=> @t622 @t620))))))))) % 0.80/1.08 (assume @p279 (forall @t615 (=> @t584 @t617))) % 0.80/1.08 (assume @p280 (forall @t322 (=> @t620 @t618))) % 0.80/1.08 (assume @p281 (forall @t322 (=> @t319 @t506))) % 0.80/1.08 (assume @p282 (forall @t322 (or @t506 @t618))) % 0.80/1.08 (assume @p283 (forall @t322 (=> @t506 (=> @t618 @t319)))) % 0.80/1.08 (assume @p284 (= @t595 (lambda (@list @t359 @t624) (and (_ (_ tptp.ord_less_eq_nat @t359) @t624) (_ (_ tptp.ord_less_eq_nat @t624) @t359))))) % 0.80/1.08 (assume @p285 (forall @t632 (=> @t584 (=> @t631 @t629)))) % 0.80/1.08 (assume @p286 (forall @t636 (=> @t635 @t634))) % 0.80/1.08 (assume @p287 (forall @t632 (=> @t584 (=> (_ (_ tptp.ord_less_eq_nat @t630) @t596) @t629)))) % 0.80/1.08 (assume @p288 (forall @t636 (=> (_ @t583 @t630) @t634))) % 0.80/1.08 (assume @p289 (forall @t587 (=> @t639 @t637))) % 0.80/1.08 (assume @p290 (forall @t612 (=> @t641 @t637))) % 0.80/1.08 (assume @p291 (forall @t322 (= @t646 (or @t643 @t319)))) % 0.80/1.08 (assume @p292 (forall @t599 (=> @t639 @t649))) % 0.80/1.08 (assume @p293 (forall @t605 (=> (forall @t603 (=> (_ (_ tptp.ord_less_nat @t54) @t600) @t602)) (=> (forall @t56 (_ @t601 @t54)) @t604)))) % 0.80/1.08 (assume @p294 (= (lambda (@list @t654) (exists @t284 (_ @t654 @t283))) (lambda (@list @t651) (exists @t653 (and (_ @t651 @t652) (forall (@list @t650) (=> (_ (_ tptp.ord_less_nat @t650) @t652) (not (_ @t651 @t650))))))))) % 0.80/1.08 (assume @p295 (forall @t322 (=> @t645 @t655))) % 0.80/1.08 (assume @p296 (forall @t615 (=> @t641 @t658))) % 0.80/1.08 (assume @p297 (forall @t606 (not (_ @t640 @t40)))) % 0.80/1.08 (assume @p298 (forall @t322 (=> @t646 (=> @t659 @t643)))) % 0.80/1.08 (assume @p299 (forall (@list @t318 @t317 @t660) (=> @t645 (=> @t643 @t660)))) % 0.80/1.08 (assume @p300 (forall @t322 (=> @t645 (not (= @t317 @t318))))) % 0.80/1.08 (assume @p301 (forall @t619 (=> @t655 (= @t646 @t319)))) % 0.80/1.08 (assume @p302 (forall (@list @t344 @t40) (=> (forall @t555 (=> (forall (@list @t661) (=> (_ (_ tptp.ord_less_nat @t661) @t553) (_ @t344 @t661))) @t570)) @t345))) % 0.80/1.08 (assume @p303 (forall @t322 (=> @t645 @t659))) % 0.80/1.08 (assume @p304 (forall @t587 (=> @t639 (not @t641)))) % 0.80/1.08 (assume @p305 (forall @t615 (=> @t641 (=> @t614 @t656)))) % 0.80/1.08 (assume @p306 (forall @t615 (=> @t582 @t658))) % 0.80/1.08 (assume @p307 (forall @t558 (not (_ @t644 @t318)))) % 0.80/1.08 (assume @p308 (forall @t322 (or @t645 @t319 @t643))) % 0.80/1.08 (assume @p309 (forall @t611 (=> @t645 (=> (_ @t642 @t607) (_ @t644 @t607))))) % 0.80/1.08 (assume @p310 (forall @t612 (=> @t641 (not @t639)))) % 0.80/1.08 (assume @p311 (forall @t322 (= @t659 (or @t645 @t643)))) % 0.80/1.08 (assume @p312 (forall @t322 (=> @t659 (=> @t646 @t643)))) % 0.80/1.08 (assume @p313 (forall @t558 (exists (@list @t662) (_ @t644 @t662)))) % 0.80/1.08 (assume @p314 (forall @t632 (=> @t641 (=> (_ (_ tptp.ord_less_nat @t630) @t596) @t665)))) % 0.80/1.08 (assume @p315 (forall @t636 (=> (_ @t640 @t630) @t666))) % 0.80/1.08 (assume @p316 (forall @t632 (=> @t641 (=> @t631 @t665)))) % 0.80/1.08 (assume @p317 (forall @t636 (=> @t635 @t666))) % 0.80/1.08 (assume @p318 (forall @t682 (=> @t681 (=> @t679 (exists @t563 (forall @t456 (=> @t674 @t673))))))) % 0.80/1.08 (assume @p319 (forall @t682 (=> @t681 (=> @t679 (exists @t563 (forall @t456 (=> @t674 @t683))))))) % 0.80/1.08 (assume @p320 (forall @t564 (exists @t563 (forall @t456 (=> @t674 @t684))))) % 0.80/1.08 (assume @p321 (forall @t564 (exists @t563 (forall @t456 (=> @t674 (not @t685)))))) % 0.80/1.08 (assume @p322 (forall @t564 (exists @t563 (forall @t456 (=> @t674 @t686))))) % 0.80/1.08 (assume @p323 (forall @t682 (=> @t689 (=> @t688 (exists @t563 (forall @t456 (=> @t562 @t673))))))) % 0.80/1.08 (assume @p324 (forall @t682 (=> @t689 (=> @t688 (exists @t563 (forall @t456 (=> @t562 @t683))))))) % 0.80/1.08 (assume @p325 (forall @t564 (exists @t563 (forall @t456 (=> @t562 @t684))))) % 0.80/1.08 (assume @p326 (forall @t564 (exists @t563 (forall @t456 (=> @t562 @t685))))) % 0.80/1.08 (assume @p327 (forall @t564 (exists @t563 (forall @t456 (=> @t562 (not @t686)))))) % 0.80/1.08 (assume @p328 (forall @t612 (=> @t637 (=> @t584 @t641)))) % 0.80/1.08 (assume @p329 (forall @t587 (=> @t639 @t586))) % 0.80/1.08 (assume @p330 (= tptp.ord_less_eq_nat (lambda @t691 (or (_ (_ tptp.ord_less_nat @t588) @t589) @t690)))) % 0.80/1.08 (assume @p331 (forall @t612 (=> @t641 @t584))) % 0.80/1.08 (assume @p332 (forall @t599 (=> @t639 (=> @t598 @t648)))) % 0.80/1.08 (assume @p333 (forall @t599 (=> @t586 @t649))) % 0.80/1.08 (assume @p334 (= tptp.ord_less_nat (lambda @t592 (and @t590 @t692)))) % 0.80/1.08 (assume @p335 (= tptp.ord_less_eq_nat (lambda @t592 (or (_ (_ tptp.ord_less_nat @t589) @t588) @t690)))) % 0.80/1.08 (assume @p336 @t695) % 0.80/1.08 (assume @p337 true) % 0.80/1.08 (step @p338 (= tptp.hilber2037636820comp_a @t697) :rule refl :args (@t697)) % 0.80/1.08 (step @p339 (= tptp.bij_betw_a_a @t702) :rule refl :args (@t702)) % 0.80/1.08 (step @p340 (= tptp.bij_betw_list_a_a @t707) :rule refl :args (@t707)) % 0.80/1.08 (step @p341 (= tptp.bij_betw_a_list_a @t712) :rule refl :args (@t712)) % 0.80/1.08 (step @p342 (= tptp.bij_be94573046list_a @t717) :rule refl :args (@t717)) % 0.80/1.08 (step @p343 (= tptp.bij_betw_nat_nat @t721) :rule refl :args (@t721)) % 0.80/1.08 (step @p344 (= tptp.list_ex_a @t724) :rule refl :args (@t724)) % 0.80/1.08 (step @p345 (= tptp.list_ex_set_a @t726) :rule refl :args (@t726)) % 0.80/1.08 (step @p346 (= tptp.ord_less_eq_set_a @t729) :rule refl :args (@t729)) % 0.80/1.08 (step @p347 (= tptp.ord_le1301786372list_a @t732) :rule refl :args (@t732)) % 0.80/1.08 (step @p348 (= tptp.ord_less_eq_o_nat @t735) :rule refl :args (@t735)) % 0.80/1.08 (step @p349 (= tptp.ord_less_nat @t736) :rule refl :args (@t736)) % 0.80/1.08 (step @p350 :rule eq-symm :args (@t737 @t738)) % 0.80/1.08 (step @p351 :rule refl :args (@t738)) % 0.80/1.08 (step @p352 :rule refl :args (@t1)) % 0.80/1.08 (step @p353 :rule cong :premises (@p352 @p351) :args ((= @t1 @t738))) % 0.80/1.08 (step @p354 :rule symm :premises (@p353)) % 0.80/1.08 (step @p355 :rule eq_resolve :premises (@p352 @p354)) % 0.80/1.08 (step @p356 :rule refl :args (@t737)) % 0.80/1.08 (step @p357 :rule refl :args (@t2)) % 0.80/1.08 (step @p358 :rule cong :premises (@p357 @p356) :args ((= @t2 @t737))) % 0.80/1.08 (step @p359 :rule symm :premises (@p358)) % 0.80/1.08 (step @p360 :rule eq_resolve :premises (@p357 @p359)) % 0.80/1.08 (step @p361 :rule cong :premises (@p360 @p355) :args (@t3)) % 0.80/1.08 (step @p362 :rule trans :premises (@p361 @p350)) % 0.80/1.08 (step @p363 :rule eq_resolve :premises (@p1 @p362)) % 0.80/1.08 (step @p364 :rule refl :args (@t739)) % 0.80/1.08 (step @p365 :rule refl :args (@t693)) % 0.80/1.08 (step @p366 :rule cong :premises (@p365 @p364) :args ((= @t693 @t739))) % 0.80/1.08 (step @p367 :rule symm :premises (@p366)) % 0.80/1.08 (step @p368 :rule eq_resolve :premises (@p365 @p367)) % 0.80/1.08 (step @p369 :rule refl :args (@t740)) % 0.80/1.08 (step @p370 :rule refl :args (@t4)) % 0.80/1.08 (step @p371 :rule cong :premises (@p370 @p369) :args ((= @t4 @t740))) % 0.80/1.08 (step @p372 :rule symm :premises (@p371)) % 0.80/1.08 (step @p373 :rule eq_resolve :premises (@p370 @p372)) % 0.80/1.08 (step @p374 :rule cong :premises (@p373 @p368) :args (@t741)) % 0.80/1.08 (step @p375 :rule cong :premises (@p374) :args ((not @t741))) % 0.80/1.08 (step @p376 :rule refl :args (@t693)) % 0.80/1.08 (step @p377 :rule cong :premises (@p3 @p376) :args (@t694)) % 0.80/1.08 (step @p378 :rule cong :premises (@p377) :args (@t695)) % 0.80/1.08 (step @p379 :rule trans :premises (@p378 @p375)) % 0.80/1.08 (step @p380 :rule eq_resolve :premises (@p336 @p379)) % 0.80/1.08 (step @p381 :rule refl :args ((tptp.comm_m543484931mset_a @t80))) % 0.80/1.08 (step @p382 :rule refl :args (@t742)) % 0.80/1.08 (step @p383 :rule cong :premises (@p382) :args (@t743)) % 0.80/1.08 (step @p384 :rule trans :premises (@p383 @p381)) % 0.80/1.08 (step @p385 :rule refl :args (tptp.comm_m543484931mset_a)) % 0.80/1.08 (step @p386 :rule ho_cong :premises (@p385 @p382)) % 0.80/1.08 (step @p387 :rule cong :premises (@p386 @p384) :args ((= (_ tptp.comm_m543484931mset_a @t742) @t743))) % 0.80/1.08 (step @p388 :rule symm :premises (@p387)) % 0.80/1.08 (step @p389 :rule refl :args (@t81)) % 0.80/1.08 (step @p390 :rule eq_resolve :premises (@p389 @p388)) % 0.80/1.08 (step @p391 :rule refl :args (@t80)) % 0.80/1.08 (step @p392 :rule cong :premises (@p391 @p382) :args ((= @t80 @t742))) % 0.80/1.08 (step @p393 :rule symm :premises (@p392)) % 0.80/1.08 (step @p394 :rule eq_resolve :premises (@p391 @p393)) % 0.80/1.08 (step @p395 :rule ho_cong :premises (@p385 @p394)) % 0.80/1.08 (step @p396 :rule trans :premises (@p395 @p390)) % 0.80/1.08 (step @p397 :rule refl :args (@t744)) % 0.80/1.08 (step @p398 :rule refl :args (@t68)) % 0.80/1.08 (step @p399 :rule cong :premises (@p398 @p397) :args ((= @t68 @t744))) % 0.80/1.08 (step @p400 :rule symm :premises (@p399)) % 0.80/1.08 (step @p401 :rule eq_resolve :premises (@p398 @p400)) % 0.80/1.08 (step @p402 :rule cong :premises (@p401 @p396) :args (@t745)) % 0.80/1.08 (step @p403 :rule cong :premises (@p402) :args ((forall @t70 @t745))) % 0.80/1.08 (step @p404 :rule eq-symm :args (@t81 @t68)) % 0.80/1.08 (step @p405 :rule cong :premises (@p404) :args (@t82)) % 0.80/1.08 (step @p406 :rule trans :premises (@p405 @p403)) % 0.80/1.08 (step @p407 :rule eq_resolve :premises (@p25 @p406)) % 0.80/1.08 (step @p408 :rule instantiate :premises (@p407) :args ((@list tptp.qs2))) % 0.80/1.08 (step @p409 :rule instantiate :premises (@p407) :args ((@list tptp.qs))) % 0.80/1.08 (step @p410 :rule refl :args (@t748)) % 0.80/1.08 (step @p411 :rule refl :args (@t750)) % 0.80/1.08 (step @p412 :rule bool-double-not-elim :args (@t751)) % 0.80/1.08 (step @p413 :rule refl :args (@t753)) % 0.80/1.08 (step @p414 :rule nary_cong :premises (@p413 @p412 @p411 @p410) :args ((or @t753 (not @t754) @t750 @t748))) % 0.80/1.08 (assume-push @p436 @t752) % 0.80/1.08 (assume-push @p437 @t754) % 0.80/1.08 (assume-push @p438 @t749) % 0.80/1.08 (step @p418 :rule false_intro :premises (@p380)) % 0.80/1.08 (step @p419 :rule symm :premises (@p408)) % 0.80/1.08 (step @p420 :rule cong :premises (@p363) :args (@t746)) % 0.80/1.08 (step @p421 :rule trans :premises (@p420 @p419)) % 0.80/1.08 (step @p422 :rule refl :args (@t740)) % 0.80/1.08 (step @p423 :rule cong :premises (@p422 @p421) :args (@t747)) % 0.80/1.08 (step @p424 :rule trans :premises (@p423 @p418)) % 0.80/1.08 (step @p425 :rule false_elim :premises (@p424)) % 0.80/1.08 (step-pop @p439 :rule scope :premises (@p425)) % 0.80/1.08 (step-pop @p440 :rule scope :premises (@p439)) % 0.80/1.08 (step-pop @p441 :rule scope :premises (@p440)) % 0.80/1.08 (step @p426 :rule process_scope :premises (@p441) :args (@t748)) % 0.80/1.08 (step @p430 :rule implies_elim :premises (@p426)) % 0.80/1.08 (step @p431 :rule cnf_and_neg :args (@t755)) % 0.80/1.08 (step @p432 :rule resolution :premises (@p431 @p430) :args (true @t755)) % 0.80/1.08 (step @p433 :rule eq_resolve :premises (@p432 @p414)) % 0.80/1.08 (step @p434 :rule reordering :premises (@p433) :args ((or @t751 @t753 @t750 @t748))) % 0.80/1.08 (step @p435 false :rule chain_m_resolution :premises (@p434 @p409 @p408 @p380 @p363) :args (false (@list false false true false) (@list @t747 @t749 @t751 @t752))) % 0.80/1.08 ) % 0.80/1.08 % SZS output end Proof % 0.80/1.08 % cvc5 exiting %------------------------------------------------------------------------------