%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU548^2 : TPTP v9.2.0. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:01:53 PM UTC 2025 % Result : Theorem 3.77s 4.00s % Output : Proof 3.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU548^2 : TPTP v9.2.0. Bugfixed v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n018.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 : Fri Oct 3 05:06:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.77/4.00 SZS status Theorem for theBenchmark.p % 3.77/4.00 SZS output start Proof for theBenchmark.p % 3.77/4.00 Clause #1 (by assumption #[]): Eq (Not (inCongP → ∀ (A B : Iota), Eq A B → ∀ (Xx Xy : Iota), Eq Xx Xy → Iff (in Xx A) (in Xy B))) True % 3.77/4.00 Clause #24 (by clausification #[1]): Eq (inCongP → ∀ (A B : Iota), Eq A B → ∀ (Xx Xy : Iota), Eq Xx Xy → Iff (in Xx A) (in Xy B)) False % 3.77/4.00 Clause #26 (by clausification #[24]): Eq (∀ (A B : Iota), Eq A B → ∀ (Xx Xy : Iota), Eq Xx Xy → Iff (in Xx A) (in Xy B)) False % 3.77/4.00 Clause #48 (by clausification #[26]): ∀ (a : Iota), % 3.77/4.00 Eq (Not (∀ (B : Iota), Eq (skS.0 4 a) B → ∀ (Xx Xy : Iota), Eq Xx Xy → Iff (in Xx (skS.0 4 a)) (in Xy B))) True % 3.77/4.00 Clause #49 (by clausification #[48]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (skS.0 4 a) B → ∀ (Xx Xy : Iota), Eq Xx Xy → Iff (in Xx (skS.0 4 a)) (in Xy B)) False % 3.77/4.00 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 3.77/4.00 Eq % 3.77/4.00 (Not % 3.77/4.00 (Eq (skS.0 4 a) (skS.0 5 a a_1) → ∀ (Xx Xy : Iota), Eq Xx Xy → Iff (in Xx (skS.0 4 a)) (in Xy (skS.0 5 a a_1)))) % 3.77/4.00 True % 3.77/4.00 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 3.77/4.00 Eq (Eq (skS.0 4 a) (skS.0 5 a a_1) → ∀ (Xx Xy : Iota), Eq Xx Xy → Iff (in Xx (skS.0 4 a)) (in Xy (skS.0 5 a a_1))) % 3.77/4.00 False % 3.77/4.00 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 4 a) (skS.0 5 a a_1)) True % 3.77/4.00 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (∀ (Xx Xy : Iota), Eq Xx Xy → Iff (in Xx (skS.0 4 a)) (in Xy (skS.0 5 a a_1))) False % 3.77/4.00 Clause #54 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (skS.0 4 a) (skS.0 5 a a_1) % 3.77/4.00 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 3.77/4.00 Eq (Not (∀ (Xy : Iota), Eq (skS.0 6 a a_1 a_2) Xy → Iff (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) (in Xy (skS.0 5 a a_1)))) % 3.77/4.00 True % 3.77/4.00 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 3.77/4.00 Eq (∀ (Xy : Iota), Eq (skS.0 6 a a_1 a_2) Xy → Iff (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) (in Xy (skS.0 5 a a_1))) False % 3.77/4.00 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/4.00 Eq % 3.77/4.00 (Not % 3.77/4.00 (Eq (skS.0 6 a a_1 a_2) (skS.0 7 a a_1 a_2 a_3) → % 3.77/4.00 Iff (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) (in (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1)))) % 3.77/4.00 True % 3.77/4.00 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/4.00 Eq % 3.77/4.00 (Eq (skS.0 6 a a_1 a_2) (skS.0 7 a a_1 a_2 a_3) → % 3.77/4.00 Iff (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) (in (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1))) % 3.77/4.00 False % 3.77/4.00 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Eq (skS.0 6 a a_1 a_2) (skS.0 7 a a_1 a_2 a_3)) True % 3.77/4.00 Clause #60 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/4.00 Eq (Iff (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) (in (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1))) False % 3.77/4.00 Clause #61 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 6 a a_1 a_2) (skS.0 7 a a_1 a_2 a_3) % 3.77/4.00 Clause #65 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/4.00 Or (Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) False) (Eq (in (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1)) False) % 3.77/4.00 Clause #66 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/4.00 Or (Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) True) (Eq (in (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1)) True) % 3.77/4.00 Clause #67 (by forward demodulation #[65, 54]): ∀ (a a_1 a_2 a_3 : Iota), % 3.77/4.00 Or (Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) False) (Eq (in (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a)) False) % 3.77/4.00 Clause #68 (by forward demodulation #[67, 61]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) False) (Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) False) % 3.77/4.00 Clause #69 (by eliminate duplicate literals #[68]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) False % 3.77/4.00 Clause #71 (by forward demodulation #[66, 69]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq False True) (Eq (in (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1)) True) % 3.77/4.00 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 7 a a_1 a_2 a_3) (skS.0 5 a a_1)) True % 3.77/4.00 Clause #73 (by forward demodulation #[72, 54]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 7 a a_1 a_2 a_3) (skS.0 4 a)) True % 3.77/4.00 Clause #74 (by forward demodulation #[73, 61]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) True % 3.77/4.00 Clause #75 (by superposition #[74, 69]): Eq True False % 3.77/4.00 Clause #76 (by clausification #[75]): False % 3.77/4.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------