%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET927+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:00:42 PM UTC 2025 % Result : Theorem 3.98s 4.14s % Output : Proof 3.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET927+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n008.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 13:48:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.98/4.14 SZS status Theorem for theBenchmark.p % 3.98/4.14 SZS output start Proof for theBenchmark.p % 3.98/4.14 Clause #4 (by assumption #[]): Eq % 3.98/4.14 (Not % 3.98/4.14 (∀ (A B C : Iota), % 3.98/4.14 Iff (Eq (set_difference (unordered_pair A B) C) (singleton A)) (And (Not (in A C)) (Or (in B C) (Eq A B))))) % 3.98/4.14 True % 3.98/4.14 Clause #5 (by assumption #[]): Eq % 3.98/4.14 (∀ (A B C : Iota), % 3.98/4.14 Iff (Eq (set_difference (unordered_pair A B) C) (singleton A)) (And (Not (in A C)) (Or (in B C) (Eq A B)))) % 3.98/4.14 True % 3.98/4.14 Clause #17 (by clausification #[5]): ∀ (a : Iota), % 3.98/4.14 Eq % 3.98/4.14 (∀ (B C : Iota), % 3.98/4.14 Iff (Eq (set_difference (unordered_pair a B) C) (singleton a)) (And (Not (in a C)) (Or (in B C) (Eq a B)))) % 3.98/4.14 True % 3.98/4.14 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 3.98/4.14 Eq % 3.98/4.14 (∀ (C : Iota), % 3.98/4.14 Iff (Eq (set_difference (unordered_pair a a_1) C) (singleton a)) (And (Not (in a C)) (Or (in a_1 C) (Eq a a_1)))) % 3.98/4.14 True % 3.98/4.14 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Eq % 3.98/4.14 (Iff (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) % 3.98/4.14 (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1)))) % 3.98/4.14 True % 3.98/4.14 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Or (Eq (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) True) % 3.98/4.14 (Eq (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1))) False) % 3.98/4.14 Clause #21 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Or (Eq (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) False) % 3.98/4.14 (Eq (And (Not (in a a_2)) (Or (in a_1 a_2) (Eq a a_1))) True) % 3.98/4.14 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Or (Eq (And (Not (in a a_1)) (Or (in a_2 a_1) (Eq a a_2))) False) % 3.98/4.14 (Eq (set_difference (unordered_pair a a_2) a_1) (singleton a)) % 3.98/4.14 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) % 3.98/4.14 (Or (Eq (Not (in a a_2)) False) (Eq (Or (in a_1 a_2) (Eq a a_1)) False)) % 3.98/4.14 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) % 3.98/4.14 (Or (Eq (Or (in a_1 a_2) (Eq a a_1)) False) (Eq (in a a_2) True)) % 3.98/4.14 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a a_2) True) (Eq (Eq a a_1) False)) % 3.98/4.14 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a a_2) True) (Eq (in a_1 a_2) False)) % 3.98/4.14 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Or (Eq (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a a_2) True) (Ne a a_1)) % 3.98/4.14 Clause #28 (by destructive equality resolution #[27]): ∀ (a a_1 : Iota), Or (Eq (set_difference (unordered_pair a a) a_1) (singleton a)) (Eq (in a a_1) True) % 3.98/4.14 Clause #29 (by clausification #[4]): Eq % 3.98/4.14 (∀ (A B C : Iota), % 3.98/4.14 Iff (Eq (set_difference (unordered_pair A B) C) (singleton A)) (And (Not (in A C)) (Or (in B C) (Eq A B)))) % 3.98/4.14 False % 3.98/4.14 Clause #30 (by clausification #[29]): ∀ (a : Iota), % 3.98/4.14 Eq % 3.98/4.14 (Not % 3.98/4.14 (∀ (B C : Iota), % 3.98/4.14 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) B) C) (singleton (skS.0 2 a))) % 3.98/4.14 (And (Not (in (skS.0 2 a) C)) (Or (in B C) (Eq (skS.0 2 a) B))))) % 3.98/4.14 True % 3.98/4.14 Clause #31 (by clausification #[30]): ∀ (a : Iota), % 3.98/4.14 Eq % 3.98/4.14 (∀ (B C : Iota), % 3.98/4.14 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) B) C) (singleton (skS.0 2 a))) % 3.98/4.14 (And (Not (in (skS.0 2 a) C)) (Or (in B C) (Eq (skS.0 2 a) B)))) % 3.98/4.14 False % 3.98/4.14 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 3.98/4.14 Eq % 3.98/4.14 (Not % 3.98/4.14 (∀ (C : Iota), % 3.98/4.14 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) (singleton (skS.0 2 a))) % 3.98/4.14 (And (Not (in (skS.0 2 a) C)) (Or (in (skS.0 3 a a_1) C) (Eq (skS.0 2 a) (skS.0 3 a a_1)))))) % 3.98/4.14 True % 3.98/4.14 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), % 3.98/4.14 Eq % 3.98/4.14 (∀ (C : Iota), % 3.98/4.14 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) (singleton (skS.0 2 a))) % 3.98/4.14 (And (Not (in (skS.0 2 a) C)) (Or (in (skS.0 3 a a_1) C) (Eq (skS.0 2 a) (skS.0 3 a a_1))))) % 3.98/4.14 False % 3.98/4.14 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Eq % 3.98/4.16 (Not % 3.98/4.16 (Iff % 3.98/4.16 (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 3.98/4.16 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1)))))) % 3.98/4.16 True % 3.98/4.16 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Eq % 3.98/4.16 (Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 3.98/4.16 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))))) % 3.98/4.16 False % 3.98/4.16 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or % 3.98/4.16 (Eq (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 False) % 3.98/4.16 (Eq % 3.98/4.16 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 3.98/4.16 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1)))) % 3.98/4.16 False) % 3.98/4.16 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or % 3.98/4.16 (Eq (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 True) % 3.98/4.16 (Eq % 3.98/4.16 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 3.98/4.16 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1)))) % 3.98/4.16 True) % 3.98/4.16 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or % 3.98/4.16 (Eq % 3.98/4.16 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 3.98/4.16 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1)))) % 3.98/4.16 False) % 3.98/4.16 (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 (Or (Eq (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) False) % 3.98/4.16 (Eq (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))) False)) % 3.98/4.16 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 (Or (Eq (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))) False) % 3.98/4.16 (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True)) % 3.98/4.16 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) False)) % 3.98/4.16 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False)) % 3.98/4.16 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.16 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Ne (skS.0 2 a) (skS.0 3 a a_1))) % 3.98/4.16 Clause #44 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or (Eq (And (Not (in a a_1)) (Or (in a_2 a_1) (Eq a a_2))) True) % 3.98/4.16 (Ne (set_difference (unordered_pair a a_2) a_1) (singleton a)) % 3.98/4.16 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Eq (Or (in a_1 a_2) (Eq a a_1)) True) % 3.98/4.16 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Eq (Not (in a a_2)) True) % 3.98/4.16 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a_1 a_2) True) (Eq (Eq a a_1) True)) % 3.98/4.16 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 3.98/4.16 Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Or (Eq (in a_1 a_2) True) (Eq a a_1)) % 3.98/4.19 Clause #50 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Ne (set_difference (unordered_pair a a_1) a_2) (singleton a)) (Eq (in a a_2) False) % 3.98/4.19 Clause #53 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or % 3.98/4.19 (Eq % 3.98/4.19 (And (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) % 3.98/4.19 (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1)))) % 3.98/4.19 True) % 3.98/4.19 (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 (Eq (Or (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) (Eq (skS.0 2 a) (skS.0 3 a a_1))) True) % 3.98/4.19 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 (Eq (Not (in (skS.0 2 a) (skS.0 4 a a_1 a_2))) True) % 3.98/4.19 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 (Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) (Eq (Eq (skS.0 2 a) (skS.0 3 a a_1)) True)) % 3.98/4.19 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 (Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) (Eq (skS.0 2 a) (skS.0 3 a a_1))) % 3.98/4.19 Clause #58 (by forward contextual literal cutting #[57, 48]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.98/4.19 Clause #60 (by superposition #[58, 26]): ∀ (a a_1 a_2 a_3 : Iota), % 3.98/4.19 Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.98/4.19 (Or (Eq (set_difference (unordered_pair a_2 (skS.0 3 a a_1)) (skS.0 4 a a_1 a_3)) (singleton a_2)) % 3.98/4.19 (Or (Eq (in a_2 (skS.0 4 a a_1 a_3)) True) (Eq True False))) % 3.98/4.19 Clause #62 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False) % 3.98/4.19 Clause #63 (by forward contextual literal cutting #[62, 50]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False % 3.98/4.19 Clause #64 (by backward demodulation #[63, 43]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 (Or (Eq False True) (Ne (skS.0 2 a) (skS.0 3 a a_1))) % 3.98/4.19 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 (Ne (skS.0 2 a) (skS.0 3 a a_1)) % 3.98/4.19 Clause #66 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 3.98/4.19 Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.98/4.19 (Or (Eq (set_difference (unordered_pair a_2 (skS.0 3 a a_1)) (skS.0 4 a a_1 a_3)) (singleton a_2)) % 3.98/4.19 (Eq (in a_2 (skS.0 4 a a_1 a_3)) True)) % 3.98/4.19 Clause #73 (by forward demodulation #[42, 63]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 (Or (Eq False True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False)) % 3.98/4.19 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a))) % 3.98/4.19 (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False) % 3.98/4.19 Clause #75 (by superposition #[74, 66]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.98/4.19 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 3.98/4.19 (Or (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False))) % 3.98/4.19 Clause #80 (by eliminate resolved literals #[75]): ∀ (a a_1 a_2 : Iota), % 3.98/4.19 Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.98/4.19 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False)) % 3.98/4.20 Clause #81 (by forward demodulation #[80, 63]): ∀ (a a_1 a_2 : Iota), % 3.98/4.20 Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) (Or (Eq False True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False)) % 3.98/4.20 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False) % 3.98/4.20 Clause #83 (by superposition #[82, 58]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) (Or (Eq False True) (Eq (skS.0 2 a) (skS.0 3 a a_1))) % 3.98/4.20 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), Or (Eq (skS.0 2 a) (skS.0 3 a a_1)) (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.98/4.20 Clause #85 (by eliminate duplicate literals #[84]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1) % 3.98/4.20 Clause #94 (by backward contextual literal cutting #[85, 65]): ∀ (a a_1 a_2 : Iota), % 3.98/4.20 Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)) % 3.98/4.20 Clause #96 (by forward demodulation #[94, 85]): ∀ (a a_1 a_2 : Iota), % 3.98/4.20 Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 2 a)) (skS.0 4 a a_1 a_2)) (singleton (skS.0 2 a)) % 3.98/4.20 Clause #97 (by superposition #[96, 28]): ∀ (a a_1 a_2 : Iota), % 3.98/4.20 Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Ne (singleton (skS.0 2 a)) (singleton (skS.0 2 a))) % 3.98/4.20 Clause #98 (by eliminate resolved literals #[97]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 3.98/4.20 Clause #99 (by superposition #[98, 63]): Eq True False % 3.98/4.20 Clause #102 (by clausification #[99]): False % 3.98/4.20 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------