%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NLP266_23 : TPTP v9.2.0. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 : Fri Oct 3 07:55:59 PM UTC 2025 % Result : Theorem 4.07s 4.25s % Output : Proof 4.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NLP266_23 : TPTP v9.2.0. Released v8.2.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 09:51:23 EDT 2025 % 0.13/0.34 % CPUTime : % 4.07/4.25 SZS status Theorem for theBenchmark.p % 4.07/4.25 SZS output start Proof for theBenchmark.p % 4.07/4.25 Clause #0 (by assumption #[]): Eq (∀ (W V : «$ki_world»), «$ki_accessible» W V) True % 4.07/4.25 Clause #1 (by assumption #[]): Eq (∀ (W : «$ki_world») (X : Iota), «$ki_exists_in_world_$i» W X) True % 4.07/4.25 Clause #3 (by assumption #[]): Eq % 4.07/4.25 (∀ (W : «$ki_world»), % 4.07/4.25 «$ki_accessible» «$ki_local_world» W → % 4.07/4.25 Exists fun I => % 4.07/4.25 And («$ki_exists_in_world_$i» W I) % 4.07/4.25 (∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → And (userid W0 u I) (string W0 I))) % 4.07/4.25 True % 4.07/4.25 Clause #4 (by assumption #[]): Eq % 4.07/4.25 (Exists fun B => % 4.07/4.25 And («$ki_exists_in_world_$i» «$ki_local_world» B) % 4.07/4.25 (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → And (entry_box W B) (number W B one))) % 4.07/4.25 True % 4.07/4.25 Clause #5 (by assumption #[]): Eq % 4.07/4.25 (∀ (W : «$ki_world»), % 4.07/4.25 «$ki_accessible» «$ki_local_world» W → % 4.07/4.25 ∀ (S : Iota), % 4.07/4.25 «$ki_exists_in_world_$i» W S → % 4.07/4.25 ∀ (I : Iota), % 4.07/4.25 «$ki_exists_in_world_$i» W I → % 4.07/4.25 ∀ (B : Iota), % 4.07/4.25 «$ki_exists_in_world_$i» W B → % 4.07/4.25 And (string W I) (entry_box W B) → % 4.07/4.25 Exists fun A => % 4.07/4.25 And («$ki_exists_in_world_$i» W A) % 4.07/4.25 (∀ (W0 : «$ki_world»), % 4.07/4.25 «$ki_accessible» W W0 → % 4.07/4.25 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 I B S2)) % 4.07/4.25 True % 4.07/4.25 Clause #6 (by assumption #[]): Eq % 4.07/4.25 (Not % 4.07/4.25 (∀ (W : «$ki_world»), % 4.07/4.25 «$ki_accessible» «$ki_local_world» W → % 4.07/4.25 Exists fun I => % 4.07/4.25 And («$ki_exists_in_world_$i» W I) % 4.07/4.25 (Exists fun B => % 4.07/4.25 And («$ki_exists_in_world_$i» W B) % 4.07/4.25 (Exists fun A => % 4.07/4.25 And («$ki_exists_in_world_$i» W A) % 4.07/4.25 (Exists fun S => % 4.07/4.25 And % 4.07/4.25 (And («$ki_exists_in_world_$i» W S) % 4.07/4.25 (∀ (W0 : «$ki_world»), % 4.07/4.25 «$ki_accessible» W W0 → And (And (userid W0 u I) (entry_box W0 B)) (number W0 B one))) % 4.07/4.25 (∀ (W0 : «$ki_world»), % 4.07/4.25 «$ki_accessible» W W0 → % 4.07/4.25 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 I B S2)))))) % 4.07/4.25 True % 4.07/4.25 Clause #7 (by clausification #[1]): ∀ (a : «$ki_world»), Eq (∀ (X : Iota), «$ki_exists_in_world_$i» a X) True % 4.07/4.25 Clause #8 (by clausification #[7]): ∀ (a : «$ki_world») (a_1 : Iota), Eq («$ki_exists_in_world_$i» a a_1) True % 4.07/4.25 Clause #9 (by clausification #[0]): ∀ (a : «$ki_world»), Eq (∀ (V : «$ki_world»), «$ki_accessible» a V) True % 4.07/4.25 Clause #10 (by clausification #[9]): ∀ (a a_1 : «$ki_world»), Eq («$ki_accessible» a a_1) True % 4.07/4.25 Clause #14 (by clausification #[4]): ∀ (a : Iota), % 4.07/4.25 Eq % 4.07/4.25 (And («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 1 a)) % 4.07/4.25 (∀ (W : «$ki_world»), % 4.07/4.25 «$ki_accessible» «$ki_local_world» W → And (entry_box W (skS.0 1 a)) (number W (skS.0 1 a) one))) % 4.07/4.25 True % 4.07/4.25 Clause #15 (by clausification #[14]): ∀ (a : Iota), % 4.07/4.25 Eq % 4.07/4.25 (∀ (W : «$ki_world»), % 4.07/4.25 «$ki_accessible» «$ki_local_world» W → And (entry_box W (skS.0 1 a)) (number W (skS.0 1 a) one)) % 4.07/4.25 True % 4.07/4.25 Clause #17 (by clausification #[15]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.07/4.25 Eq («$ki_accessible» «$ki_local_world» a → And (entry_box a (skS.0 1 a_1)) (number a (skS.0 1 a_1) one)) True % 4.07/4.25 Clause #18 (by clausification #[17]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.07/4.25 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.07/4.25 (Eq (And (entry_box a (skS.0 1 a_1)) (number a (skS.0 1 a_1) one)) True) % 4.07/4.25 Clause #19 (by clausification #[18]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.07/4.25 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (number a (skS.0 1 a_1) one) True) % 4.07/4.25 Clause #20 (by clausification #[18]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.07/4.25 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (entry_box a (skS.0 1 a_1)) True) % 4.07/4.25 Clause #21 (by forward demodulation #[19, 10]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (number a (skS.0 1 a_1) one) True) % 4.09/4.27 Clause #22 (by clausification #[21]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (number a (skS.0 1 a_1) one) True % 4.09/4.27 Clause #23 (by clausification #[3]): ∀ (a : «$ki_world»), % 4.09/4.27 Eq % 4.09/4.27 («$ki_accessible» «$ki_local_world» a → % 4.09/4.27 Exists fun I => % 4.09/4.27 And («$ki_exists_in_world_$i» a I) % 4.09/4.27 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (userid W0 u I) (string W0 I))) % 4.09/4.27 True % 4.09/4.27 Clause #24 (by clausification #[23]): ∀ (a : «$ki_world»), % 4.09/4.27 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.27 (Eq % 4.09/4.27 (Exists fun I => % 4.09/4.27 And («$ki_exists_in_world_$i» a I) % 4.09/4.27 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (userid W0 u I) (string W0 I))) % 4.09/4.27 True) % 4.09/4.27 Clause #25 (by clausification #[24]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.09/4.27 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.27 (Eq % 4.09/4.27 (And («$ki_exists_in_world_$i» a (skS.0 2 a a_1)) % 4.09/4.27 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (userid W0 u (skS.0 2 a a_1)) (string W0 (skS.0 2 a a_1)))) % 4.09/4.27 True) % 4.09/4.27 Clause #26 (by clausification #[25]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.09/4.27 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.27 (Eq (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (userid W0 u (skS.0 2 a a_1)) (string W0 (skS.0 2 a a_1))) % 4.09/4.27 True) % 4.09/4.27 Clause #28 (by clausification #[26]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), % 4.09/4.27 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.27 (Eq («$ki_accessible» a a_1 → And (userid a_1 u (skS.0 2 a a_2)) (string a_1 (skS.0 2 a a_2))) True) % 4.09/4.27 Clause #29 (by clausification #[28]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), % 4.09/4.27 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.27 (Or (Eq («$ki_accessible» a a_1) False) (Eq (And (userid a_1 u (skS.0 2 a a_2)) (string a_1 (skS.0 2 a a_2))) True)) % 4.09/4.27 Clause #30 (by clausification #[29]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), % 4.09/4.27 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.27 (Or (Eq («$ki_accessible» a a_1) False) (Eq (string a_1 (skS.0 2 a a_2)) True)) % 4.09/4.27 Clause #31 (by clausification #[29]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), % 4.09/4.27 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.27 (Or (Eq («$ki_accessible» a a_1) False) (Eq (userid a_1 u (skS.0 2 a a_2)) True)) % 4.09/4.27 Clause #32 (by forward demodulation #[30, 10]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), % 4.09/4.27 Or (Eq True False) (Or (Eq («$ki_accessible» a a_1) False) (Eq (string a_1 (skS.0 2 a a_2)) True)) % 4.09/4.27 Clause #33 (by clausification #[32]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Or (Eq («$ki_accessible» a a_1) False) (Eq (string a_1 (skS.0 2 a a_2)) True) % 4.09/4.27 Clause #34 (by forward demodulation #[33, 10]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Or (Eq True False) (Eq (string a (skS.0 2 a_1 a_2)) True) % 4.09/4.27 Clause #35 (by clausification #[34]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Eq (string a (skS.0 2 a_1 a_2)) True % 4.09/4.27 Clause #36 (by forward demodulation #[20, 10]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (entry_box a (skS.0 1 a_1)) True) % 4.09/4.27 Clause #37 (by clausification #[36]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (entry_box a (skS.0 1 a_1)) True % 4.09/4.27 Clause #40 (by forward demodulation #[31, 10]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), % 4.09/4.27 Or (Eq True False) (Or (Eq («$ki_accessible» a a_1) False) (Eq (userid a_1 u (skS.0 2 a a_2)) True)) % 4.09/4.27 Clause #41 (by clausification #[40]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Or (Eq («$ki_accessible» a a_1) False) (Eq (userid a_1 u (skS.0 2 a a_2)) True) % 4.09/4.27 Clause #42 (by forward demodulation #[41, 10]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Or (Eq True False) (Eq (userid a u (skS.0 2 a_1 a_2)) True) % 4.09/4.27 Clause #43 (by clausification #[42]): ∀ (a a_1 : «$ki_world») (a_2 : Iota), Eq (userid a u (skS.0 2 a_1 a_2)) True % 4.09/4.27 Clause #44 (by clausification #[5]): ∀ (a : «$ki_world»), % 4.09/4.27 Eq % 4.09/4.27 («$ki_accessible» «$ki_local_world» a → % 4.09/4.27 ∀ (S : Iota), % 4.09/4.27 «$ki_exists_in_world_$i» a S → % 4.09/4.29 ∀ (I : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a I → % 4.09/4.29 ∀ (B : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a B → % 4.09/4.29 And (string a I) (entry_box a B) → % 4.09/4.29 Exists fun A => % 4.09/4.29 And («$ki_exists_in_world_$i» a A) % 4.09/4.29 (∀ (W0 : «$ki_world»), % 4.09/4.29 «$ki_accessible» a W0 → % 4.09/4.29 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 I B S2)) % 4.09/4.29 True % 4.09/4.29 Clause #45 (by clausification #[44]): ∀ (a : «$ki_world»), % 4.09/4.29 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.29 (Eq % 4.09/4.29 (∀ (S : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a S → % 4.09/4.29 ∀ (I : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a I → % 4.09/4.29 ∀ (B : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a B → % 4.09/4.29 And (string a I) (entry_box a B) → % 4.09/4.29 Exists fun A => % 4.09/4.29 And («$ki_exists_in_world_$i» a A) % 4.09/4.29 (∀ (W0 : «$ki_world»), % 4.09/4.29 «$ki_accessible» a W0 → % 4.09/4.29 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 I B S2)) % 4.09/4.29 True) % 4.09/4.29 Clause #46 (by clausification #[45]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.09/4.29 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.29 (Eq % 4.09/4.29 («$ki_exists_in_world_$i» a a_1 → % 4.09/4.29 ∀ (I : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a I → % 4.09/4.29 ∀ (B : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a B → % 4.09/4.29 And (string a I) (entry_box a B) → % 4.09/4.29 Exists fun A => % 4.09/4.29 And («$ki_exists_in_world_$i» a A) % 4.09/4.29 (∀ (W0 : «$ki_world»), % 4.09/4.29 «$ki_accessible» a W0 → % 4.09/4.29 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 A S2 → in W0 I B S2)) % 4.09/4.29 True) % 4.09/4.29 Clause #47 (by clausification #[46]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.09/4.29 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.29 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.09/4.29 (Eq % 4.09/4.29 (∀ (I : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a I → % 4.09/4.29 ∀ (B : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a B → % 4.09/4.29 And (string a I) (entry_box a B) → % 4.09/4.29 Exists fun A => % 4.09/4.29 And («$ki_exists_in_world_$i» a A) % 4.09/4.29 (∀ (W0 : «$ki_world»), % 4.09/4.29 «$ki_accessible» a W0 → % 4.09/4.29 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 A S2 → in W0 I B S2)) % 4.09/4.29 True)) % 4.09/4.29 Clause #48 (by clausification #[47]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.09/4.29 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.29 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.09/4.29 (Eq % 4.09/4.29 («$ki_exists_in_world_$i» a a_2 → % 4.09/4.29 ∀ (B : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a B → % 4.09/4.29 And (string a a_2) (entry_box a B) → % 4.09/4.29 Exists fun A => % 4.09/4.29 And («$ki_exists_in_world_$i» a A) % 4.09/4.29 (∀ (W0 : «$ki_world»), % 4.09/4.29 «$ki_accessible» a W0 → % 4.09/4.29 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 A S2 → in W0 a_2 B S2)) % 4.09/4.29 True)) % 4.09/4.29 Clause #49 (by clausification #[48]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.09/4.29 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.29 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.09/4.29 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.09/4.29 (Eq % 4.09/4.29 (∀ (B : Iota), % 4.09/4.29 «$ki_exists_in_world_$i» a B → % 4.09/4.29 And (string a a_2) (entry_box a B) → % 4.09/4.29 Exists fun A => % 4.09/4.29 And («$ki_exists_in_world_$i» a A) % 4.09/4.29 (∀ (W0 : «$ki_world»), % 4.09/4.29 «$ki_accessible» a W0 → % 4.09/4.29 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 A S2 → in W0 a_2 B S2)) % 4.09/4.29 True))) % 4.09/4.29 Clause #50 (by clausification #[49]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota), % 4.09/4.30 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.09/4.30 (Eq % 4.09/4.30 («$ki_exists_in_world_$i» a a_3 → % 4.09/4.30 And (string a a_2) (entry_box a a_3) → % 4.09/4.30 Exists fun A => % 4.09/4.30 And («$ki_exists_in_world_$i» a A) % 4.09/4.30 (∀ (W0 : «$ki_world»), % 4.09/4.30 «$ki_accessible» a W0 → % 4.09/4.30 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 A S2 → in W0 a_2 a_3 S2)) % 4.09/4.30 True))) % 4.09/4.30 Clause #51 (by clausification #[50]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota), % 4.09/4.30 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.09/4.30 (Eq % 4.09/4.30 (And (string a a_2) (entry_box a a_3) → % 4.09/4.30 Exists fun A => % 4.09/4.30 And («$ki_exists_in_world_$i» a A) % 4.09/4.30 (∀ (W0 : «$ki_world»), % 4.09/4.30 «$ki_accessible» a W0 → % 4.09/4.30 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 A S2 → in W0 a_2 a_3 S2)) % 4.09/4.30 True)))) % 4.09/4.30 Clause #52 (by clausification #[51]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota), % 4.09/4.30 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.09/4.30 (Or (Eq (And (string a a_2) (entry_box a a_3)) False) % 4.09/4.30 (Eq % 4.09/4.30 (Exists fun A => % 4.09/4.30 And («$ki_exists_in_world_$i» a A) % 4.09/4.30 (∀ (W0 : «$ki_world»), % 4.09/4.30 «$ki_accessible» a W0 → % 4.09/4.30 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 A S2 → in W0 a_2 a_3 S2)) % 4.09/4.30 True))))) % 4.09/4.30 Clause #53 (by clausification #[52]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota), % 4.09/4.30 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.09/4.30 (Or % 4.09/4.30 (Eq % 4.09/4.30 (Exists fun A => % 4.09/4.30 And («$ki_exists_in_world_$i» a A) % 4.09/4.30 (∀ (W0 : «$ki_world»), % 4.09/4.30 «$ki_accessible» a W0 → % 4.09/4.30 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 A S2 → in W0 a_2 a_3 S2)) % 4.09/4.30 True) % 4.09/4.30 (Or (Eq (string a a_2) False) (Eq (entry_box a a_3) False)))))) % 4.09/4.30 Clause #54 (by clausification #[53]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota), % 4.09/4.30 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.09/4.30 (Or (Eq (string a a_2) False) % 4.09/4.30 (Or (Eq (entry_box a a_3) False) % 4.09/4.30 (Eq % 4.09/4.30 (And («$ki_exists_in_world_$i» a (skS.0 3 a a_1 a_2 a_3 a_4)) % 4.09/4.30 (∀ (W0 : «$ki_world»), % 4.09/4.30 «$ki_accessible» a W0 → % 4.09/4.30 ∀ (S2 : Iota), % 4.09/4.30 «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 (skS.0 3 a a_1 a_2 a_3 a_4) S2 → in W0 a_2 a_3 S2)) % 4.09/4.30 True)))))) % 4.09/4.30 Clause #55 (by clausification #[54]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota), % 4.09/4.30 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.09/4.30 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.09/4.30 (Or (Eq (string a a_2) False) % 4.09/4.30 (Or (Eq (entry_box a a_3) False) % 4.09/4.30 (Eq % 4.09/4.30 (∀ (W0 : «$ki_world»), % 4.09/4.30 «$ki_accessible» a W0 → % 4.09/4.30 ∀ (S2 : Iota), % 4.15/4.32 «$ki_exists_in_world_$i» W0 S2 → do W0 a_1 (skS.0 3 a a_1 a_2 a_3 a_4) S2 → in W0 a_2 a_3 S2) % 4.15/4.32 True)))))) % 4.15/4.32 Clause #57 (by clausification #[55]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 : Iota), % 4.15/4.32 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.15/4.32 (Or (Eq (string a a_2) False) % 4.15/4.32 (Or (Eq (entry_box a a_3) False) % 4.15/4.32 (Eq % 4.15/4.32 («$ki_accessible» a a_4 → % 4.15/4.32 ∀ (S2 : Iota), % 4.15/4.32 «$ki_exists_in_world_$i» a_4 S2 → do a_4 a_1 (skS.0 3 a a_1 a_2 a_3 a_5) S2 → in a_4 a_2 a_3 S2) % 4.15/4.32 True)))))) % 4.15/4.32 Clause #58 (by clausification #[57]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 : Iota), % 4.15/4.32 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.15/4.32 (Or (Eq (string a a_2) False) % 4.15/4.32 (Or (Eq (entry_box a a_3) False) % 4.15/4.32 (Or (Eq («$ki_accessible» a a_4) False) % 4.15/4.32 (Eq % 4.15/4.32 (∀ (S2 : Iota), % 4.15/4.32 «$ki_exists_in_world_$i» a_4 S2 → do a_4 a_1 (skS.0 3 a a_1 a_2 a_3 a_5) S2 → in a_4 a_2 a_3 S2) % 4.15/4.32 True))))))) % 4.15/4.32 Clause #59 (by clausification #[58]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 : Iota), % 4.15/4.32 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.15/4.32 (Or (Eq (string a a_2) False) % 4.15/4.32 (Or (Eq (entry_box a a_3) False) % 4.15/4.32 (Or (Eq («$ki_accessible» a a_4) False) % 4.15/4.32 (Eq («$ki_exists_in_world_$i» a_4 a_5 → do a_4 a_1 (skS.0 3 a a_1 a_2 a_3 a_6) a_5 → in a_4 a_2 a_3 a_5) % 4.15/4.32 True))))))) % 4.15/4.32 Clause #60 (by clausification #[59]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 : Iota), % 4.15/4.32 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.15/4.32 (Or (Eq (string a a_2) False) % 4.15/4.32 (Or (Eq (entry_box a a_3) False) % 4.15/4.32 (Or (Eq («$ki_accessible» a a_4) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a_4 a_5) False) % 4.15/4.32 (Eq (do a_4 a_1 (skS.0 3 a a_1 a_2 a_3 a_6) a_5 → in a_4 a_2 a_3 a_5) True)))))))) % 4.15/4.32 Clause #61 (by clausification #[60]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 : Iota), % 4.15/4.32 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.15/4.32 (Or (Eq (string a a_2) False) % 4.15/4.32 (Or (Eq (entry_box a a_3) False) % 4.15/4.32 (Or (Eq («$ki_accessible» a a_4) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a_4 a_5) False) % 4.15/4.32 (Or (Eq (do a_4 a_1 (skS.0 3 a a_1 a_2 a_3 a_6) a_5) False) (Eq (in a_4 a_2 a_3 a_5) True))))))))) % 4.15/4.32 Clause #62 (by forward demodulation #[61, 10]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 : Iota), % 4.15/4.32 Or (Eq True False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.15/4.32 (Or (Eq (string a a_2) False) % 4.15/4.32 (Or (Eq (entry_box a a_3) False) % 4.15/4.32 (Or (Eq («$ki_accessible» a a_4) False) % 4.15/4.32 (Or (Eq («$ki_exists_in_world_$i» a_4 a_5) False) % 4.15/4.32 (Or (Eq (do a_4 a_1 (skS.0 3 a a_1 a_2 a_3 a_6) a_5) False) (Eq (in a_4 a_2 a_3 a_5) True))))))))) % 4.15/4.34 Clause #63 (by clausification #[62]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 : Iota), % 4.15/4.34 Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a a_3) False) % 4.15/4.34 (Or (Eq (string a a_2) False) % 4.15/4.34 (Or (Eq (entry_box a a_3) False) % 4.15/4.34 (Or (Eq («$ki_accessible» a a_4) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a_4 a_5) False) % 4.15/4.34 (Or (Eq (do a_4 a_1 (skS.0 3 a a_1 a_2 a_3 a_6) a_5) False) (Eq (in a_4 a_2 a_3 a_5) True)))))))) % 4.15/4.34 Clause #64 (by forward demodulation #[63, 8]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.34 Or (Eq True False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.15/4.34 (Or (Eq (string a a_1) False) % 4.15/4.34 (Or (Eq (entry_box a a_2) False) % 4.15/4.34 (Or (Eq («$ki_accessible» a a_3) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a_3 a_4) False) % 4.15/4.34 (Or (Eq (do a_3 a_5 (skS.0 3 a a_5 a_1 a_2 a_6) a_4) False) (Eq (in a_3 a_1 a_2 a_4) True)))))))) % 4.15/4.34 Clause #65 (by clausification #[64]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.34 Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a a_2) False) % 4.15/4.34 (Or (Eq (string a a_1) False) % 4.15/4.34 (Or (Eq (entry_box a a_2) False) % 4.15/4.34 (Or (Eq («$ki_accessible» a a_3) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a_3 a_4) False) % 4.15/4.34 (Or (Eq (do a_3 a_5 (skS.0 3 a a_5 a_1 a_2 a_6) a_4) False) (Eq (in a_3 a_1 a_2 a_4) True))))))) % 4.15/4.34 Clause #66 (by forward demodulation #[65, 8]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.34 Or (Eq True False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.34 (Or (Eq (string a a_2) False) % 4.15/4.34 (Or (Eq (entry_box a a_1) False) % 4.15/4.34 (Or (Eq («$ki_accessible» a a_3) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a_3 a_4) False) % 4.15/4.34 (Or (Eq (do a_3 a_5 (skS.0 3 a a_5 a_2 a_1 a_6) a_4) False) (Eq (in a_3 a_2 a_1 a_4) True))))))) % 4.15/4.34 Clause #67 (by clausification #[66]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.34 Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 4.15/4.34 (Or (Eq (string a a_2) False) % 4.15/4.34 (Or (Eq (entry_box a a_1) False) % 4.15/4.34 (Or (Eq («$ki_accessible» a a_3) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a_3 a_4) False) % 4.15/4.34 (Or (Eq (do a_3 a_5 (skS.0 3 a a_5 a_2 a_1 a_6) a_4) False) (Eq (in a_3 a_2 a_1 a_4) True)))))) % 4.15/4.34 Clause #68 (by forward demodulation #[67, 8]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.34 Or (Eq True False) % 4.15/4.34 (Or (Eq (string a a_1) False) % 4.15/4.34 (Or (Eq (entry_box a a_2) False) % 4.15/4.34 (Or (Eq («$ki_accessible» a a_3) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a_3 a_4) False) % 4.15/4.34 (Or (Eq (do a_3 a_5 (skS.0 3 a a_5 a_1 a_2 a_6) a_4) False) (Eq (in a_3 a_1 a_2 a_4) True)))))) % 4.15/4.34 Clause #69 (by clausification #[68]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.34 Or (Eq (string a a_1) False) % 4.15/4.34 (Or (Eq (entry_box a a_2) False) % 4.15/4.34 (Or (Eq («$ki_accessible» a a_3) False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a_3 a_4) False) % 4.15/4.34 (Or (Eq (do a_3 a_5 (skS.0 3 a a_5 a_1 a_2 a_6) a_4) False) (Eq (in a_3 a_1 a_2 a_4) True))))) % 4.15/4.34 Clause #70 (by forward demodulation #[69, 10]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.34 Or (Eq (string a a_1) False) % 4.15/4.34 (Or (Eq (entry_box a a_2) False) % 4.15/4.34 (Or (Eq True False) % 4.15/4.34 (Or (Eq («$ki_exists_in_world_$i» a_3 a_4) False) % 4.15/4.34 (Or (Eq (do a_3 a_5 (skS.0 3 a a_5 a_1 a_2 a_6) a_4) False) (Eq (in a_3 a_1 a_2 a_4) True))))) % 4.15/4.34 Clause #71 (by clausification #[70]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.36 Or (Eq (string a a_1) False) % 4.15/4.36 (Or (Eq (entry_box a a_2) False) % 4.15/4.36 (Or (Eq («$ki_exists_in_world_$i» a_3 a_4) False) % 4.15/4.36 (Or (Eq (do a_3 a_5 (skS.0 3 a a_5 a_1 a_2 a_6) a_4) False) (Eq (in a_3 a_1 a_2 a_4) True)))) % 4.15/4.36 Clause #72 (by forward demodulation #[71, 8]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.36 Or (Eq (string a a_1) False) % 4.15/4.36 (Or (Eq (entry_box a a_2) False) % 4.15/4.36 (Or (Eq True False) (Or (Eq (do a_3 a_4 (skS.0 3 a a_4 a_1 a_2 a_5) a_6) False) (Eq (in a_3 a_1 a_2 a_6) True)))) % 4.15/4.36 Clause #73 (by clausification #[72]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 a_6 : Iota), % 4.15/4.36 Or (Eq (string a a_1) False) % 4.15/4.36 (Or (Eq (entry_box a a_2) False) % 4.15/4.36 (Or (Eq (do a_3 a_4 (skS.0 3 a a_4 a_1 a_2 a_5) a_6) False) (Eq (in a_3 a_1 a_2 a_6) True))) % 4.15/4.36 Clause #74 (by superposition #[73, 35]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 a_7 : Iota), % 4.15/4.36 Or (Eq (entry_box a a_1) False) % 4.15/4.36 (Or (Eq (do a_2 a_3 (skS.0 3 a a_3 (skS.0 2 a_4 a_5) a_1 a_6) a_7) False) % 4.15/4.36 (Or (Eq (in a_2 (skS.0 2 a_4 a_5) a_1 a_7) True) (Eq False True))) % 4.15/4.36 Clause #83 (by clausification #[6]): Eq % 4.15/4.36 (∀ (W : «$ki_world»), % 4.15/4.36 «$ki_accessible» «$ki_local_world» W → % 4.15/4.36 Exists fun I => % 4.15/4.36 And («$ki_exists_in_world_$i» W I) % 4.15/4.36 (Exists fun B => % 4.15/4.36 And («$ki_exists_in_world_$i» W B) % 4.15/4.36 (Exists fun A => % 4.15/4.36 And («$ki_exists_in_world_$i» W A) % 4.15/4.36 (Exists fun S => % 4.15/4.36 And % 4.15/4.36 (And («$ki_exists_in_world_$i» W S) % 4.15/4.36 (∀ (W0 : «$ki_world»), % 4.15/4.36 «$ki_accessible» W W0 → And (And (userid W0 u I) (entry_box W0 B)) (number W0 B one))) % 4.15/4.36 (∀ (W0 : «$ki_world»), % 4.15/4.36 «$ki_accessible» W W0 → % 4.15/4.36 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 I B S2))))) % 4.15/4.36 False % 4.15/4.36 Clause #84 (by clausification #[83]): ∀ (a : «$ki_world»), % 4.15/4.36 Eq % 4.15/4.36 (Not % 4.15/4.36 («$ki_accessible» «$ki_local_world» (skS.0 4 a) → % 4.15/4.36 Exists fun I => % 4.15/4.36 And («$ki_exists_in_world_$i» (skS.0 4 a) I) % 4.15/4.36 (Exists fun B => % 4.15/4.36 And («$ki_exists_in_world_$i» (skS.0 4 a) B) % 4.15/4.36 (Exists fun A => % 4.15/4.36 And («$ki_exists_in_world_$i» (skS.0 4 a) A) % 4.15/4.36 (Exists fun S => % 4.15/4.36 And % 4.15/4.36 (And («$ki_exists_in_world_$i» (skS.0 4 a) S) % 4.15/4.36 (∀ (W0 : «$ki_world»), % 4.15/4.36 «$ki_accessible» (skS.0 4 a) W0 → % 4.15/4.36 And (And (userid W0 u I) (entry_box W0 B)) (number W0 B one))) % 4.15/4.36 (∀ (W0 : «$ki_world»), % 4.15/4.36 «$ki_accessible» (skS.0 4 a) W0 → % 4.15/4.36 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 I B S2)))))) % 4.15/4.36 True % 4.15/4.36 Clause #85 (by clausification #[84]): ∀ (a : «$ki_world»), % 4.15/4.36 Eq % 4.15/4.36 («$ki_accessible» «$ki_local_world» (skS.0 4 a) → % 4.15/4.36 Exists fun I => % 4.15/4.36 And («$ki_exists_in_world_$i» (skS.0 4 a) I) % 4.15/4.36 (Exists fun B => % 4.15/4.36 And («$ki_exists_in_world_$i» (skS.0 4 a) B) % 4.15/4.36 (Exists fun A => % 4.15/4.36 And («$ki_exists_in_world_$i» (skS.0 4 a) A) % 4.15/4.36 (Exists fun S => % 4.15/4.36 And % 4.15/4.36 (And («$ki_exists_in_world_$i» (skS.0 4 a) S) % 4.15/4.36 (∀ (W0 : «$ki_world»), % 4.15/4.36 «$ki_accessible» (skS.0 4 a) W0 → % 4.15/4.36 And (And (userid W0 u I) (entry_box W0 B)) (number W0 B one))) % 4.15/4.36 (∀ (W0 : «$ki_world»), % 4.15/4.36 «$ki_accessible» (skS.0 4 a) W0 → % 4.15/4.36 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 I B S2))))) % 4.15/4.36 False % 4.15/4.36 Clause #87 (by clausification #[85]): ∀ (a : «$ki_world»), % 4.15/4.37 Eq % 4.15/4.37 (Exists fun I => % 4.15/4.37 And («$ki_exists_in_world_$i» (skS.0 4 a) I) % 4.15/4.37 (Exists fun B => % 4.15/4.37 And («$ki_exists_in_world_$i» (skS.0 4 a) B) % 4.15/4.37 (Exists fun A => % 4.15/4.37 And («$ki_exists_in_world_$i» (skS.0 4 a) A) % 4.15/4.37 (Exists fun S => % 4.15/4.37 And % 4.15/4.37 (And («$ki_exists_in_world_$i» (skS.0 4 a) S) % 4.15/4.37 (∀ (W0 : «$ki_world»), % 4.15/4.37 «$ki_accessible» (skS.0 4 a) W0 → And (And (userid W0 u I) (entry_box W0 B)) (number W0 B one))) % 4.15/4.37 (∀ (W0 : «$ki_world»), % 4.15/4.37 «$ki_accessible» (skS.0 4 a) W0 → % 4.15/4.37 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 I B S2))))) % 4.15/4.37 False % 4.15/4.37 Clause #88 (by clausification #[74]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 a_7 : Iota), % 4.15/4.37 Or (Eq (entry_box a a_1) False) % 4.15/4.37 (Or (Eq (do a_2 a_3 (skS.0 3 a a_3 (skS.0 2 a_4 a_5) a_1 a_6) a_7) False) % 4.15/4.37 (Eq (in a_2 (skS.0 2 a_4 a_5) a_1 a_7) True)) % 4.15/4.37 Clause #89 (by superposition #[88, 37]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 a_3 : «$ki_world») (a_4 a_5 a_6 a_7 : Iota), % 4.15/4.37 Or (Eq (do a a_1 (skS.0 3 a_2 a_1 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) a_7) False) % 4.15/4.37 (Or (Eq (in a (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_7) True) (Eq False True)) % 4.15/4.37 Clause #90 (by clausification #[89]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 a_3 : «$ki_world») (a_4 a_5 a_6 a_7 : Iota), % 4.15/4.37 Or (Eq (do a a_1 (skS.0 3 a_2 a_1 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) a_7) False) % 4.15/4.37 (Eq (in a (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_7) True) % 4.15/4.37 Clause #91 (by clausification #[87]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.15/4.37 Eq % 4.15/4.37 (And («$ki_exists_in_world_$i» (skS.0 4 a) a_1) % 4.15/4.37 (Exists fun B => % 4.15/4.37 And («$ki_exists_in_world_$i» (skS.0 4 a) B) % 4.15/4.37 (Exists fun A => % 4.15/4.37 And («$ki_exists_in_world_$i» (skS.0 4 a) A) % 4.15/4.37 (Exists fun S => % 4.15/4.37 And % 4.15/4.37 (And («$ki_exists_in_world_$i» (skS.0 4 a) S) % 4.15/4.37 (∀ (W0 : «$ki_world»), % 4.15/4.37 «$ki_accessible» (skS.0 4 a) W0 → And (And (userid W0 u a_1) (entry_box W0 B)) (number W0 B one))) % 4.15/4.37 (∀ (W0 : «$ki_world»), % 4.15/4.37 «$ki_accessible» (skS.0 4 a) W0 → % 4.15/4.37 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 a_1 B S2))))) % 4.15/4.37 False % 4.15/4.37 Clause #92 (by clausification #[91]): ∀ (a : «$ki_world») (a_1 : Iota), % 4.15/4.37 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.15/4.37 (Eq % 4.15/4.37 (Exists fun B => % 4.15/4.37 And («$ki_exists_in_world_$i» (skS.0 4 a) B) % 4.15/4.37 (Exists fun A => % 4.15/4.37 And («$ki_exists_in_world_$i» (skS.0 4 a) A) % 4.15/4.37 (Exists fun S => % 4.15/4.37 And % 4.15/4.37 (And («$ki_exists_in_world_$i» (skS.0 4 a) S) % 4.15/4.37 (∀ (W0 : «$ki_world»), % 4.15/4.37 «$ki_accessible» (skS.0 4 a) W0 → And (And (userid W0 u a_1) (entry_box W0 B)) (number W0 B one))) % 4.15/4.37 (∀ (W0 : «$ki_world»), % 4.15/4.37 «$ki_accessible» (skS.0 4 a) W0 → % 4.15/4.37 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 a_1 B S2)))) % 4.15/4.37 False) % 4.15/4.37 Clause #93 (by clausification #[92]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.15/4.37 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.15/4.37 (Eq % 4.15/4.37 (And («$ki_exists_in_world_$i» (skS.0 4 a) a_2) % 4.15/4.37 (Exists fun A => % 4.15/4.37 And («$ki_exists_in_world_$i» (skS.0 4 a) A) % 4.15/4.37 (Exists fun S => % 4.15/4.37 And % 4.15/4.37 (And («$ki_exists_in_world_$i» (skS.0 4 a) S) % 4.15/4.37 (∀ (W0 : «$ki_world»), % 4.15/4.37 «$ki_accessible» (skS.0 4 a) W0 → % 4.15/4.37 And (And (userid W0 u a_1) (entry_box W0 a_2)) (number W0 a_2 one))) % 4.15/4.37 (∀ (W0 : «$ki_world»), % 4.15/4.37 «$ki_accessible» (skS.0 4 a) W0 → % 4.15/4.37 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 a_1 a_2 S2)))) % 4.21/4.39 False) % 4.21/4.39 Clause #94 (by clausification #[93]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 4.21/4.39 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.39 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.39 (Eq % 4.21/4.39 (Exists fun A => % 4.21/4.39 And («$ki_exists_in_world_$i» (skS.0 4 a) A) % 4.21/4.39 (Exists fun S => % 4.21/4.39 And % 4.21/4.39 (And («$ki_exists_in_world_$i» (skS.0 4 a) S) % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → % 4.21/4.39 And (And (userid W0 u a_1) (entry_box W0 a_2)) (number W0 a_2 one))) % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → % 4.21/4.39 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S A S2 → in W0 a_1 a_2 S2))) % 4.21/4.39 False)) % 4.21/4.39 Clause #95 (by clausification #[94]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota), % 4.21/4.39 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.39 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.39 (Eq % 4.21/4.39 (And («$ki_exists_in_world_$i» (skS.0 4 a) a_3) % 4.21/4.39 (Exists fun S => % 4.21/4.39 And % 4.21/4.39 (And («$ki_exists_in_world_$i» (skS.0 4 a) S) % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → And (And (userid W0 u a_1) (entry_box W0 a_2)) (number W0 a_2 one))) % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → % 4.21/4.39 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S a_3 S2 → in W0 a_1 a_2 S2))) % 4.21/4.39 False)) % 4.21/4.39 Clause #96 (by clausification #[95]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota), % 4.21/4.39 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.39 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.39 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.39 (Eq % 4.21/4.39 (Exists fun S => % 4.21/4.39 And % 4.21/4.39 (And («$ki_exists_in_world_$i» (skS.0 4 a) S) % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → And (And (userid W0 u a_1) (entry_box W0 a_2)) (number W0 a_2 one))) % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → % 4.21/4.39 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 S a_3 S2 → in W0 a_1 a_2 S2)) % 4.21/4.39 False))) % 4.21/4.39 Clause #97 (by clausification #[96]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota), % 4.21/4.39 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.39 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.39 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.39 (Eq % 4.21/4.39 (And % 4.21/4.39 (And («$ki_exists_in_world_$i» (skS.0 4 a) a_4) % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → And (And (userid W0 u a_1) (entry_box W0 a_2)) (number W0 a_2 one))) % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → % 4.21/4.39 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_4 a_3 S2 → in W0 a_1 a_2 S2)) % 4.21/4.39 False))) % 4.21/4.39 Clause #98 (by clausification #[97]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota), % 4.21/4.39 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.39 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.39 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.39 (Or % 4.21/4.39 (Eq % 4.21/4.39 (And («$ki_exists_in_world_$i» (skS.0 4 a) a_4) % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → And (And (userid W0 u a_1) (entry_box W0 a_2)) (number W0 a_2 one))) % 4.21/4.39 False) % 4.21/4.39 (Eq % 4.21/4.39 (∀ (W0 : «$ki_world»), % 4.21/4.39 «$ki_accessible» (skS.0 4 a) W0 → % 4.21/4.39 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_4 a_3 S2 → in W0 a_1 a_2 S2) % 4.21/4.39 False)))) % 4.21/4.39 Clause #99 (by clausification #[98]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota), % 4.21/4.39 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.39 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.41 (Or % 4.21/4.41 (Eq % 4.21/4.41 (∀ (W0 : «$ki_world»), % 4.21/4.41 «$ki_accessible» (skS.0 4 a) W0 → % 4.21/4.41 ∀ (S2 : Iota), «$ki_exists_in_world_$i» W0 S2 → do W0 a_4 a_3 S2 → in W0 a_1 a_2 S2) % 4.21/4.41 False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.41 (Eq % 4.21/4.41 (∀ (W0 : «$ki_world»), % 4.21/4.41 «$ki_accessible» (skS.0 4 a) W0 → And (And (userid W0 u a_1) (entry_box W0 a_2)) (number W0 a_2 one)) % 4.21/4.41 False))))) % 4.21/4.41 Clause #100 (by clausification #[99]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 : «$ki_world»), % 4.21/4.41 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.41 (Or % 4.21/4.41 (Eq % 4.21/4.41 (∀ (W0 : «$ki_world»), % 4.21/4.41 «$ki_accessible» (skS.0 4 a) W0 → And (And (userid W0 u a_1) (entry_box W0 a_2)) (number W0 a_2 one)) % 4.21/4.41 False) % 4.21/4.41 (Eq % 4.21/4.41 (Not % 4.21/4.41 («$ki_accessible» (skS.0 4 a) (skS.0 5 a a_4 a_3 a_1 a_2 a_5) → % 4.21/4.41 ∀ (S2 : Iota), % 4.21/4.41 «$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_5) S2 → % 4.21/4.41 do (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_4 a_3 S2 → in (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_1 a_2 S2)) % 4.21/4.41 True))))) % 4.21/4.41 Clause #101 (by clausification #[100]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world»), % 4.21/4.41 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.41 (Or % 4.21/4.41 (Eq % 4.21/4.41 (Not % 4.21/4.41 («$ki_accessible» (skS.0 4 a) (skS.0 5 a a_4 a_3 a_1 a_2 a_5) → % 4.21/4.41 ∀ (S2 : Iota), % 4.21/4.41 «$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_5) S2 → % 4.21/4.41 do (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_4 a_3 S2 → in (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_1 a_2 S2)) % 4.21/4.41 True) % 4.21/4.41 (Eq % 4.21/4.41 (Not % 4.21/4.41 («$ki_accessible» (skS.0 4 a) (skS.0 6 a a_1 a_2 a_6) → % 4.21/4.41 And (And (userid (skS.0 6 a a_1 a_2 a_6) u a_1) (entry_box (skS.0 6 a a_1 a_2 a_6) a_2)) % 4.21/4.41 (number (skS.0 6 a a_1 a_2 a_6) a_2 one))) % 4.21/4.41 True))))) % 4.21/4.41 Clause #102 (by clausification #[101]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world»), % 4.21/4.41 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.41 (Or % 4.21/4.41 (Eq % 4.21/4.41 (Not % 4.21/4.41 («$ki_accessible» (skS.0 4 a) (skS.0 6 a a_1 a_2 a_5) → % 4.21/4.41 And (And (userid (skS.0 6 a a_1 a_2 a_5) u a_1) (entry_box (skS.0 6 a a_1 a_2 a_5) a_2)) % 4.21/4.41 (number (skS.0 6 a a_1 a_2 a_5) a_2 one))) % 4.21/4.41 True) % 4.21/4.41 (Eq % 4.21/4.41 («$ki_accessible» (skS.0 4 a) (skS.0 5 a a_4 a_3 a_1 a_2 a_6) → % 4.21/4.41 ∀ (S2 : Iota), % 4.21/4.41 «$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_6) S2 → % 4.21/4.41 do (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_4 a_3 S2 → in (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_1 a_2 S2) % 4.21/4.41 False))))) % 4.21/4.41 Clause #103 (by clausification #[102]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world»), % 4.21/4.41 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.41 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.43 (Or % 4.21/4.43 (Eq % 4.21/4.43 («$ki_accessible» (skS.0 4 a) (skS.0 5 a a_4 a_3 a_1 a_2 a_5) → % 4.21/4.43 ∀ (S2 : Iota), % 4.21/4.43 «$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_5) S2 → % 4.21/4.43 do (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_4 a_3 S2 → in (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_1 a_2 S2) % 4.21/4.43 False) % 4.21/4.43 (Eq % 4.21/4.43 («$ki_accessible» (skS.0 4 a) (skS.0 6 a a_1 a_2 a_6) → % 4.21/4.43 And (And (userid (skS.0 6 a a_1 a_2 a_6) u a_1) (entry_box (skS.0 6 a a_1 a_2 a_6) a_2)) % 4.21/4.43 (number (skS.0 6 a a_1 a_2 a_6) a_2 one)) % 4.21/4.43 False))))) % 4.21/4.43 Clause #105 (by clausification #[103]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world»), % 4.21/4.43 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.43 (Or % 4.21/4.43 (Eq % 4.21/4.43 («$ki_accessible» (skS.0 4 a) (skS.0 6 a a_1 a_2 a_5) → % 4.21/4.43 And (And (userid (skS.0 6 a a_1 a_2 a_5) u a_1) (entry_box (skS.0 6 a a_1 a_2 a_5) a_2)) % 4.21/4.43 (number (skS.0 6 a a_1 a_2 a_5) a_2 one)) % 4.21/4.43 False) % 4.21/4.43 (Eq % 4.21/4.43 (∀ (S2 : Iota), % 4.21/4.43 «$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_6) S2 → % 4.21/4.43 do (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_4 a_3 S2 → in (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_1 a_2 S2) % 4.21/4.43 False))))) % 4.21/4.43 Clause #127 (by clausification #[105]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world»), % 4.21/4.43 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.43 (Or % 4.21/4.43 (Eq % 4.21/4.43 (∀ (S2 : Iota), % 4.21/4.43 «$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_5) S2 → % 4.21/4.43 do (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_4 a_3 S2 → in (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_1 a_2 S2) % 4.21/4.43 False) % 4.21/4.43 (Eq % 4.21/4.43 (And (And (userid (skS.0 6 a a_1 a_2 a_6) u a_1) (entry_box (skS.0 6 a a_1 a_2 a_6) a_2)) % 4.21/4.43 (number (skS.0 6 a a_1 a_2 a_6) a_2 one)) % 4.21/4.43 False))))) % 4.21/4.43 Clause #140 (by clausification #[127]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.21/4.43 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.43 (Or % 4.21/4.43 (Eq % 4.21/4.43 (And (And (userid (skS.0 6 a a_1 a_2 a_5) u a_1) (entry_box (skS.0 6 a a_1 a_2 a_5) a_2)) % 4.21/4.43 (number (skS.0 6 a a_1 a_2 a_5) a_2 one)) % 4.21/4.43 False) % 4.21/4.43 (Eq % 4.21/4.43 (Not % 4.21/4.43 («$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_6) (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7) → % 4.21/4.43 do (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_4 a_3 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7) → % 4.21/4.43 in (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_1 a_2 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7))) % 4.21/4.43 True))))) % 4.21/4.43 Clause #141 (by clausification #[140]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 : «$ki_world») (a_6 : Iota) (a_7 : «$ki_world»), % 4.21/4.43 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.43 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.43 (Or % 4.21/4.43 (Eq % 4.21/4.43 (Not % 4.21/4.43 («$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_5) (skS.0 8 a a_4 a_3 a_1 a_2 a_5 a_6) → % 4.21/4.43 do (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_4 a_3 (skS.0 8 a a_4 a_3 a_1 a_2 a_5 a_6) → % 4.21/4.45 in (skS.0 5 a a_4 a_3 a_1 a_2 a_5) a_1 a_2 (skS.0 8 a a_4 a_3 a_1 a_2 a_5 a_6))) % 4.21/4.45 True) % 4.21/4.45 (Or (Eq (And (userid (skS.0 6 a a_1 a_2 a_7) u a_1) (entry_box (skS.0 6 a a_1 a_2 a_7) a_2)) False) % 4.21/4.45 (Eq (number (skS.0 6 a a_1 a_2 a_7) a_2 one) False)))))) % 4.21/4.45 Clause #142 (by clausification #[141]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.21/4.45 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.45 (Or (Eq (And (userid (skS.0 6 a a_1 a_2 a_5) u a_1) (entry_box (skS.0 6 a a_1 a_2 a_5) a_2)) False) % 4.21/4.45 (Or (Eq (number (skS.0 6 a a_1 a_2 a_5) a_2 one) False) % 4.21/4.45 (Eq % 4.21/4.45 («$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_6) (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7) → % 4.21/4.45 do (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_4 a_3 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7) → % 4.21/4.45 in (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_1 a_2 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7)) % 4.21/4.45 False)))))) % 4.21/4.45 Clause #143 (by clausification #[142]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.21/4.45 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.45 (Or (Eq (number (skS.0 6 a a_1 a_2 a_5) a_2 one) False) % 4.21/4.45 (Or % 4.21/4.45 (Eq % 4.21/4.45 («$ki_exists_in_world_$i» (skS.0 5 a a_4 a_3 a_1 a_2 a_6) (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7) → % 4.21/4.45 do (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_4 a_3 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7) → % 4.21/4.45 in (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_1 a_2 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7)) % 4.21/4.45 False) % 4.21/4.45 (Or (Eq (userid (skS.0 6 a a_1 a_2 a_5) u a_1) False) % 4.21/4.45 (Eq (entry_box (skS.0 6 a a_1 a_2 a_5) a_2) False))))))) % 4.21/4.45 Clause #145 (by clausification #[143]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.21/4.45 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.45 (Or (Eq (number (skS.0 6 a a_1 a_2 a_5) a_2 one) False) % 4.21/4.45 (Or (Eq (userid (skS.0 6 a a_1 a_2 a_5) u a_1) False) % 4.21/4.45 (Or (Eq (entry_box (skS.0 6 a a_1 a_2 a_5) a_2) False) % 4.21/4.45 (Eq % 4.21/4.45 (do (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_4 a_3 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7) → % 4.21/4.45 in (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_1 a_2 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7)) % 4.21/4.45 False))))))) % 4.21/4.45 Clause #172 (by clausification #[145]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.21/4.45 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.21/4.45 (Or (Eq (number (skS.0 6 a a_1 a_2 a_5) a_2 one) False) % 4.21/4.45 (Or (Eq (userid (skS.0 6 a a_1 a_2 a_5) u a_1) False) % 4.21/4.45 (Or (Eq (entry_box (skS.0 6 a a_1 a_2 a_5) a_2) False) % 4.21/4.45 (Eq (do (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_4 a_3 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7)) True))))))) % 4.21/4.45 Clause #173 (by clausification #[145]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.21/4.45 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.21/4.45 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_4) False) % 4.29/4.47 (Or (Eq (number (skS.0 6 a a_1 a_2 a_5) a_2 one) False) % 4.29/4.47 (Or (Eq (userid (skS.0 6 a a_1 a_2 a_5) u a_1) False) % 4.29/4.47 (Or (Eq (entry_box (skS.0 6 a a_1 a_2 a_5) a_2) False) % 4.29/4.47 (Eq (in (skS.0 5 a a_4 a_3 a_1 a_2 a_6) a_1 a_2 (skS.0 8 a a_4 a_3 a_1 a_2 a_6 a_7)) False))))))) % 4.29/4.47 Clause #174 (by forward demodulation #[172, 8]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.47 Or (Eq True False) % 4.29/4.47 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.29/4.47 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.29/4.47 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.29/4.47 (Or (Eq (number (skS.0 6 a a_4 a_1 a_5) a_1 one) False) % 4.29/4.47 (Or (Eq (userid (skS.0 6 a a_4 a_1 a_5) u a_4) False) % 4.29/4.47 (Or (Eq (entry_box (skS.0 6 a a_4 a_1 a_5) a_1) False) % 4.29/4.47 (Eq (do (skS.0 5 a a_3 a_2 a_4 a_1 a_6) a_3 a_2 (skS.0 8 a a_3 a_2 a_4 a_1 a_6 a_7)) True))))))) % 4.29/4.47 Clause #175 (by clausification #[174]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.47 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.29/4.47 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.29/4.47 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.29/4.47 (Or (Eq (number (skS.0 6 a a_4 a_1 a_5) a_1 one) False) % 4.29/4.47 (Or (Eq (userid (skS.0 6 a a_4 a_1 a_5) u a_4) False) % 4.29/4.47 (Or (Eq (entry_box (skS.0 6 a a_4 a_1 a_5) a_1) False) % 4.29/4.47 (Eq (do (skS.0 5 a a_3 a_2 a_4 a_1 a_6) a_3 a_2 (skS.0 8 a a_3 a_2 a_4 a_1 a_6 a_7)) True)))))) % 4.29/4.47 Clause #176 (by forward demodulation #[175, 8]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.47 Or (Eq True False) % 4.29/4.47 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.29/4.47 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.29/4.47 (Or (Eq (number (skS.0 6 a a_3 a_4 a_5) a_4 one) False) % 4.29/4.47 (Or (Eq (userid (skS.0 6 a a_3 a_4 a_5) u a_3) False) % 4.29/4.47 (Or (Eq (entry_box (skS.0 6 a a_3 a_4 a_5) a_4) False) % 4.29/4.47 (Eq (do (skS.0 5 a a_2 a_1 a_3 a_4 a_6) a_2 a_1 (skS.0 8 a a_2 a_1 a_3 a_4 a_6 a_7)) True)))))) % 4.29/4.47 Clause #177 (by clausification #[176]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.47 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.29/4.47 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.29/4.47 (Or (Eq (number (skS.0 6 a a_3 a_4 a_5) a_4 one) False) % 4.29/4.47 (Or (Eq (userid (skS.0 6 a a_3 a_4 a_5) u a_3) False) % 4.29/4.47 (Or (Eq (entry_box (skS.0 6 a a_3 a_4 a_5) a_4) False) % 4.29/4.47 (Eq (do (skS.0 5 a a_2 a_1 a_3 a_4 a_6) a_2 a_1 (skS.0 8 a a_2 a_1 a_3 a_4 a_6 a_7)) True))))) % 4.29/4.47 Clause #178 (by forward demodulation #[177, 8]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.47 Or (Eq True False) % 4.29/4.47 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.29/4.47 (Or (Eq (number (skS.0 6 a a_2 a_3 a_4) a_3 one) False) % 4.29/4.47 (Or (Eq (userid (skS.0 6 a a_2 a_3 a_4) u a_2) False) % 4.29/4.47 (Or (Eq (entry_box (skS.0 6 a a_2 a_3 a_4) a_3) False) % 4.29/4.47 (Eq (do (skS.0 5 a a_1 a_5 a_2 a_3 a_6) a_1 a_5 (skS.0 8 a a_1 a_5 a_2 a_3 a_6 a_7)) True))))) % 4.29/4.47 Clause #179 (by clausification #[178]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.47 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.29/4.47 (Or (Eq (number (skS.0 6 a a_2 a_3 a_4) a_3 one) False) % 4.29/4.47 (Or (Eq (userid (skS.0 6 a a_2 a_3 a_4) u a_2) False) % 4.29/4.47 (Or (Eq (entry_box (skS.0 6 a a_2 a_3 a_4) a_3) False) % 4.29/4.47 (Eq (do (skS.0 5 a a_1 a_5 a_2 a_3 a_6) a_1 a_5 (skS.0 8 a a_1 a_5 a_2 a_3 a_6 a_7)) True)))) % 4.29/4.47 Clause #180 (by forward demodulation #[179, 8]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.47 Or (Eq True False) % 4.29/4.47 (Or (Eq (number (skS.0 6 a a_1 a_2 a_3) a_2 one) False) % 4.29/4.47 (Or (Eq (userid (skS.0 6 a a_1 a_2 a_3) u a_1) False) % 4.29/4.49 (Or (Eq (entry_box (skS.0 6 a a_1 a_2 a_3) a_2) False) % 4.29/4.49 (Eq (do (skS.0 5 a a_4 a_5 a_1 a_2 a_6) a_4 a_5 (skS.0 8 a a_4 a_5 a_1 a_2 a_6 a_7)) True)))) % 4.29/4.49 Clause #181 (by clausification #[180]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.49 Or (Eq (number (skS.0 6 a a_1 a_2 a_3) a_2 one) False) % 4.29/4.49 (Or (Eq (userid (skS.0 6 a a_1 a_2 a_3) u a_1) False) % 4.29/4.49 (Or (Eq (entry_box (skS.0 6 a a_1 a_2 a_3) a_2) False) % 4.29/4.49 (Eq (do (skS.0 5 a a_4 a_5 a_1 a_2 a_6) a_4 a_5 (skS.0 8 a a_4 a_5 a_1 a_2 a_6 a_7)) True))) % 4.29/4.49 Clause #182 (by superposition #[181, 22]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.49 Or (Eq (userid (skS.0 6 a a_1 (skS.0 1 a_2) a_3) u a_1) False) % 4.29/4.49 (Or (Eq (entry_box (skS.0 6 a a_1 (skS.0 1 a_2) a_3) (skS.0 1 a_2)) False) % 4.29/4.49 (Or (Eq (do (skS.0 5 a a_4 a_5 a_1 (skS.0 1 a_2) a_6) a_4 a_5 (skS.0 8 a a_4 a_5 a_1 (skS.0 1 a_2) a_6 a_7)) True) % 4.29/4.49 (Eq False True))) % 4.29/4.49 Clause #183 (by clausification #[182]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.49 Or (Eq (userid (skS.0 6 a a_1 (skS.0 1 a_2) a_3) u a_1) False) % 4.29/4.49 (Or (Eq (entry_box (skS.0 6 a a_1 (skS.0 1 a_2) a_3) (skS.0 1 a_2)) False) % 4.29/4.49 (Eq (do (skS.0 5 a a_4 a_5 a_1 (skS.0 1 a_2) a_6) a_4 a_5 (skS.0 8 a a_4 a_5 a_1 (skS.0 1 a_2) a_6 a_7)) True)) % 4.29/4.49 Clause #184 (by superposition #[183, 43]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 : Iota) (a_7 : «$ki_world») (a_8 : Iota), % 4.29/4.49 Or (Eq (entry_box (skS.0 6 a (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_4) (skS.0 1 a_3)) False) % 4.29/4.49 (Or % 4.29/4.49 (Eq % 4.29/4.49 (do (skS.0 5 a a_5 a_6 (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_7) a_5 a_6 % 4.29/4.49 (skS.0 8 a a_5 a_6 (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_7 a_8)) % 4.29/4.49 True) % 4.29/4.49 (Eq False True)) % 4.29/4.49 Clause #185 (by clausification #[184]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 : Iota) (a_7 : «$ki_world») (a_8 : Iota), % 4.29/4.49 Or (Eq (entry_box (skS.0 6 a (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_4) (skS.0 1 a_3)) False) % 4.29/4.49 (Eq % 4.29/4.49 (do (skS.0 5 a a_5 a_6 (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_7) a_5 a_6 % 4.29/4.49 (skS.0 8 a a_5 a_6 (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_7 a_8)) % 4.29/4.49 True) % 4.29/4.49 Clause #186 (by superposition #[185, 37]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.49 Or % 4.29/4.49 (Eq % 4.29/4.49 (do (skS.0 5 a a_1 a_2 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) a_1 a_2 % 4.29/4.49 (skS.0 8 a a_1 a_2 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6 a_7)) % 4.29/4.49 True) % 4.29/4.49 (Eq False True) % 4.29/4.49 Clause #187 (by forward demodulation #[173, 8]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.49 Or (Eq True False) % 4.29/4.49 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.29/4.49 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.29/4.49 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.29/4.49 (Or (Eq (number (skS.0 6 a a_4 a_1 a_5) a_1 one) False) % 4.29/4.49 (Or (Eq (userid (skS.0 6 a a_4 a_1 a_5) u a_4) False) % 4.29/4.49 (Or (Eq (entry_box (skS.0 6 a a_4 a_1 a_5) a_1) False) % 4.29/4.49 (Eq (in (skS.0 5 a a_3 a_2 a_4 a_1 a_6) a_4 a_1 (skS.0 8 a a_3 a_2 a_4 a_1 a_6 a_7)) False))))))) % 4.29/4.49 Clause #188 (by clausification #[187]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.29/4.49 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.29/4.49 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.29/4.49 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_3) False) % 4.29/4.49 (Or (Eq (number (skS.0 6 a a_4 a_1 a_5) a_1 one) False) % 4.29/4.49 (Or (Eq (userid (skS.0 6 a a_4 a_1 a_5) u a_4) False) % 4.29/4.49 (Or (Eq (entry_box (skS.0 6 a a_4 a_1 a_5) a_1) False) % 4.29/4.49 (Eq (in (skS.0 5 a a_3 a_2 a_4 a_1 a_6) a_4 a_1 (skS.0 8 a a_3 a_2 a_4 a_1 a_6 a_7)) False)))))) % 4.29/4.49 Clause #189 (by forward demodulation #[188, 8]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.51 Or (Eq True False) % 4.33/4.51 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.33/4.51 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.33/4.51 (Or (Eq (number (skS.0 6 a a_3 a_4 a_5) a_4 one) False) % 4.33/4.51 (Or (Eq (userid (skS.0 6 a a_3 a_4 a_5) u a_3) False) % 4.33/4.51 (Or (Eq (entry_box (skS.0 6 a a_3 a_4 a_5) a_4) False) % 4.33/4.51 (Eq (in (skS.0 5 a a_2 a_1 a_3 a_4 a_6) a_3 a_4 (skS.0 8 a a_2 a_1 a_3 a_4 a_6 a_7)) False)))))) % 4.33/4.51 Clause #190 (by clausification #[189]): ∀ (a : «$ki_world») (a_1 a_2 a_3 a_4 : Iota) (a_5 a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.51 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.33/4.51 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_2) False) % 4.33/4.51 (Or (Eq (number (skS.0 6 a a_3 a_4 a_5) a_4 one) False) % 4.33/4.51 (Or (Eq (userid (skS.0 6 a a_3 a_4 a_5) u a_3) False) % 4.33/4.51 (Or (Eq (entry_box (skS.0 6 a a_3 a_4 a_5) a_4) False) % 4.33/4.51 (Eq (in (skS.0 5 a a_2 a_1 a_3 a_4 a_6) a_3 a_4 (skS.0 8 a a_2 a_1 a_3 a_4 a_6 a_7)) False))))) % 4.33/4.51 Clause #191 (by forward demodulation #[190, 8]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.51 Or (Eq True False) % 4.33/4.51 (Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.33/4.51 (Or (Eq (number (skS.0 6 a a_2 a_3 a_4) a_3 one) False) % 4.33/4.51 (Or (Eq (userid (skS.0 6 a a_2 a_3 a_4) u a_2) False) % 4.33/4.51 (Or (Eq (entry_box (skS.0 6 a a_2 a_3 a_4) a_3) False) % 4.33/4.51 (Eq (in (skS.0 5 a a_1 a_5 a_2 a_3 a_6) a_2 a_3 (skS.0 8 a a_1 a_5 a_2 a_3 a_6 a_7)) False))))) % 4.33/4.51 Clause #192 (by clausification #[191]): ∀ (a : «$ki_world») (a_1 a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.51 Or (Eq («$ki_exists_in_world_$i» (skS.0 4 a) a_1) False) % 4.33/4.51 (Or (Eq (number (skS.0 6 a a_2 a_3 a_4) a_3 one) False) % 4.33/4.51 (Or (Eq (userid (skS.0 6 a a_2 a_3 a_4) u a_2) False) % 4.33/4.51 (Or (Eq (entry_box (skS.0 6 a a_2 a_3 a_4) a_3) False) % 4.33/4.51 (Eq (in (skS.0 5 a a_1 a_5 a_2 a_3 a_6) a_2 a_3 (skS.0 8 a a_1 a_5 a_2 a_3 a_6 a_7)) False)))) % 4.33/4.51 Clause #193 (by forward demodulation #[192, 8]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.51 Or (Eq True False) % 4.33/4.51 (Or (Eq (number (skS.0 6 a a_1 a_2 a_3) a_2 one) False) % 4.33/4.51 (Or (Eq (userid (skS.0 6 a a_1 a_2 a_3) u a_1) False) % 4.33/4.51 (Or (Eq (entry_box (skS.0 6 a a_1 a_2 a_3) a_2) False) % 4.33/4.51 (Eq (in (skS.0 5 a a_4 a_5 a_1 a_2 a_6) a_1 a_2 (skS.0 8 a a_4 a_5 a_1 a_2 a_6 a_7)) False)))) % 4.33/4.51 Clause #194 (by clausification #[193]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.51 Or (Eq (number (skS.0 6 a a_1 a_2 a_3) a_2 one) False) % 4.33/4.51 (Or (Eq (userid (skS.0 6 a a_1 a_2 a_3) u a_1) False) % 4.33/4.51 (Or (Eq (entry_box (skS.0 6 a a_1 a_2 a_3) a_2) False) % 4.33/4.51 (Eq (in (skS.0 5 a a_4 a_5 a_1 a_2 a_6) a_1 a_2 (skS.0 8 a a_4 a_5 a_1 a_2 a_6 a_7)) False))) % 4.33/4.51 Clause #195 (by superposition #[194, 22]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.51 Or (Eq (userid (skS.0 6 a a_1 (skS.0 1 a_2) a_3) u a_1) False) % 4.33/4.51 (Or (Eq (entry_box (skS.0 6 a a_1 (skS.0 1 a_2) a_3) (skS.0 1 a_2)) False) % 4.33/4.51 (Or % 4.33/4.51 (Eq % 4.33/4.51 (in (skS.0 5 a a_4 a_5 a_1 (skS.0 1 a_2) a_6) a_1 (skS.0 1 a_2) (skS.0 8 a a_4 a_5 a_1 (skS.0 1 a_2) a_6 a_7)) % 4.33/4.51 False) % 4.33/4.51 (Eq False True))) % 4.33/4.51 Clause #196 (by clausification #[186]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.51 Eq % 4.33/4.51 (do (skS.0 5 a a_1 a_2 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) a_1 a_2 % 4.33/4.51 (skS.0 8 a a_1 a_2 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6 a_7)) % 4.33/4.51 True % 4.33/4.51 Clause #197 (by superposition #[196, 90]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 a_3 : «$ki_world») (a_4 a_5 a_6 : Iota) (a_7 : «$ki_world») (a_8 a_9 : Iota) % 4.33/4.51 (a_10 : «$ki_world») (a_11 : Iota), % 4.33/4.51 Or (Eq True False) % 4.33/4.51 (Eq % 4.33/4.51 (in (skS.0 5 a a_1 (skS.0 3 a_2 a_1 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) (skS.0 2 a_7 a_8) (skS.0 1 a_9) a_10) % 4.33/4.53 (skS.0 2 a_3 a_4) (skS.0 1 a_5) % 4.33/4.53 (skS.0 8 a a_1 (skS.0 3 a_2 a_1 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) (skS.0 2 a_7 a_8) (skS.0 1 a_9) a_10 a_11)) % 4.33/4.53 True) % 4.33/4.53 Clause #198 (by clausification #[195]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.53 Or (Eq (userid (skS.0 6 a a_1 (skS.0 1 a_2) a_3) u a_1) False) % 4.33/4.53 (Or (Eq (entry_box (skS.0 6 a a_1 (skS.0 1 a_2) a_3) (skS.0 1 a_2)) False) % 4.33/4.53 (Eq (in (skS.0 5 a a_4 a_5 a_1 (skS.0 1 a_2) a_6) a_1 (skS.0 1 a_2) (skS.0 8 a a_4 a_5 a_1 (skS.0 1 a_2) a_6 a_7)) % 4.33/4.53 False)) % 4.33/4.53 Clause #199 (by superposition #[198, 43]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 : Iota) (a_7 : «$ki_world») (a_8 : Iota), % 4.33/4.53 Or (Eq (entry_box (skS.0 6 a (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_4) (skS.0 1 a_3)) False) % 4.33/4.53 (Or % 4.33/4.53 (Eq % 4.33/4.53 (in (skS.0 5 a a_5 a_6 (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_7) (skS.0 2 a_1 a_2) (skS.0 1 a_3) % 4.33/4.53 (skS.0 8 a a_5 a_6 (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_7 a_8)) % 4.33/4.53 False) % 4.33/4.53 (Eq False True)) % 4.33/4.53 Clause #200 (by clausification #[199]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota) (a_4 : «$ki_world») (a_5 a_6 : Iota) (a_7 : «$ki_world») (a_8 : Iota), % 4.33/4.53 Or (Eq (entry_box (skS.0 6 a (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_4) (skS.0 1 a_3)) False) % 4.33/4.53 (Eq % 4.33/4.53 (in (skS.0 5 a a_5 a_6 (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_7) (skS.0 2 a_1 a_2) (skS.0 1 a_3) % 4.33/4.53 (skS.0 8 a a_5 a_6 (skS.0 2 a_1 a_2) (skS.0 1 a_3) a_7 a_8)) % 4.33/4.53 False) % 4.33/4.53 Clause #201 (by superposition #[200, 37]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.53 Or % 4.33/4.53 (Eq % 4.33/4.53 (in (skS.0 5 a a_1 a_2 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) (skS.0 2 a_3 a_4) (skS.0 1 a_5) % 4.33/4.53 (skS.0 8 a a_1 a_2 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6 a_7)) % 4.33/4.53 False) % 4.33/4.53 (Eq False True) % 4.33/4.53 Clause #202 (by clausification #[201]): ∀ (a : «$ki_world») (a_1 a_2 : Iota) (a_3 : «$ki_world») (a_4 a_5 : Iota) (a_6 : «$ki_world») (a_7 : Iota), % 4.33/4.53 Eq % 4.33/4.53 (in (skS.0 5 a a_1 a_2 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) (skS.0 2 a_3 a_4) (skS.0 1 a_5) % 4.33/4.53 (skS.0 8 a a_1 a_2 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6 a_7)) % 4.33/4.53 False % 4.33/4.53 Clause #203 (by clausification #[197]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 a_3 : «$ki_world») (a_4 a_5 a_6 : Iota) (a_7 : «$ki_world») (a_8 a_9 : Iota) % 4.33/4.53 (a_10 : «$ki_world») (a_11 : Iota), % 4.33/4.53 Eq % 4.33/4.53 (in (skS.0 5 a a_1 (skS.0 3 a_2 a_1 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) (skS.0 2 a_7 a_8) (skS.0 1 a_9) a_10) % 4.33/4.53 (skS.0 2 a_3 a_4) (skS.0 1 a_5) % 4.33/4.53 (skS.0 8 a a_1 (skS.0 3 a_2 a_1 (skS.0 2 a_3 a_4) (skS.0 1 a_5) a_6) (skS.0 2 a_7 a_8) (skS.0 1 a_9) a_10 a_11)) % 4.33/4.53 True % 4.33/4.53 Clause #204 (by superposition #[203, 202]): Eq True False % 4.33/4.53 Clause #205 (by clausification #[204]): False % 4.33/4.53 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------