%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU142+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:00:57 PM UTC 2025 % Result : Theorem 32.35s 32.53s % Output : Proof 32.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU142+1 : TPTP v9.2.0. Released v3.3.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n001.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 05:56:23 EDT 2025 % 0.12/0.34 % CPUTime : % 32.35/32.53 SZS status Theorem for theBenchmark.p % 32.35/32.53 SZS output start Proof for theBenchmark.p % 32.35/32.53 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 32.35/32.53 Clause #3 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (unordered_pair A B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D A) (Eq D B)))) True % 32.35/32.53 Clause #6 (by assumption #[]): Eq (Not (∀ (A : Iota), Eq (unordered_pair A A) (singleton A))) True % 32.35/32.53 Clause #19 (by clausification #[6]): Eq (∀ (A : Iota), Eq (unordered_pair A A) (singleton A)) False % 32.35/32.53 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (Not (Eq (unordered_pair (skS.0 1 a) (skS.0 1 a)) (singleton (skS.0 1 a)))) True % 32.35/32.53 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (Eq (unordered_pair (skS.0 1 a) (skS.0 1 a)) (singleton (skS.0 1 a))) False % 32.35/32.53 Clause #22 (by clausification #[21]): ∀ (a : Iota), Ne (unordered_pair (skS.0 1 a) (skS.0 1 a)) (singleton (skS.0 1 a)) % 32.35/32.53 Clause #26 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 32.35/32.53 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 32.35/32.53 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 32.35/32.53 Clause #36 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 32.35/32.53 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 32.35/32.53 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Eq (Eq a_2 a_1) False)) % 32.35/32.53 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq (Eq a_2 a_1) True)) % 32.35/32.53 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 32.35/32.53 Clause #41 (by destructive equality resolution #[40]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 32.35/32.53 Clause #42 (by destructive equality resolution #[41]): ∀ (a : Iota), Eq (in a (singleton a)) True % 32.35/32.53 Clause #45 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) False) (Eq a_2 a_1)) % 32.35/32.53 Clause #46 (by destructive equality resolution #[45]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) False) (Eq a a_1) % 32.35/32.53 Clause #49 (by clausification #[3]): ∀ (a : Iota), % 32.35/32.53 Eq (∀ (B C : Iota), Iff (Eq C (unordered_pair a B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D B)))) True % 32.35/32.53 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 32.35/32.53 Eq (∀ (C : Iota), Iff (Eq C (unordered_pair a a_1)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D a_1)))) True % 32.35/32.53 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 32.35/32.53 Eq (Iff (Eq a (unordered_pair a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2)))) True % 32.35/32.53 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 32.35/32.53 Or (Eq (Eq a (unordered_pair a_1 a_2)) True) (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) False) % 32.35/32.53 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 32.35/32.53 Or (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) False) (Eq a (unordered_pair a_1 a_2)) % 32.35/32.53 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota), % 32.35/32.53 Or (Eq a (unordered_pair a_1 a_2)) % 32.35/32.53 (Eq % 32.35/32.53 (Not (Iff (in (skS.0 3 a a_1 a_2 a_3) a) (Or (Eq (skS.0 3 a a_1 a_2 a_3) a_1) (Eq (skS.0 3 a a_1 a_2 a_3) a_2)))) % 32.35/32.53 True) % 32.35/32.53 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 a_3 : Iota), % 32.35/32.53 Or (Eq a (unordered_pair a_1 a_2)) % 32.35/32.53 (Eq (Iff (in (skS.0 3 a a_1 a_2 a_3) a) (Or (Eq (skS.0 3 a a_1 a_2 a_3) a_1) (Eq (skS.0 3 a a_1 a_2 a_3) a_2))) % 32.35/32.53 False) % 32.35/32.53 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 32.35/32.53 Or (Eq a (unordered_pair a_1 a_2)) % 32.35/32.53 (Or (Eq (in (skS.0 3 a a_1 a_2 a_3) a) False) % 32.35/32.53 (Eq (Or (Eq (skS.0 3 a a_1 a_2 a_3) a_1) (Eq (skS.0 3 a a_1 a_2 a_3) a_2)) False)) % 32.35/32.53 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_2)) % 32.44/32.66 (Or (Eq (in (skS.0 3 a a_1 a_2 a_3) a) True) % 32.44/32.66 (Eq (Or (Eq (skS.0 3 a a_1 a_2 a_3) a_1) (Eq (skS.0 3 a a_1 a_2 a_3) a_2)) True)) % 32.44/32.66 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_2)) % 32.44/32.66 (Or (Eq (in (skS.0 3 a a_1 a_2 a_3) a) False) (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_2) False)) % 32.44/32.66 Clause #61 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_2)) (Or (Eq (in (skS.0 3 a a_1 a_2 a_3) a) False) (Ne (skS.0 3 a a_1 a_2 a_3) a_2)) % 32.44/32.66 Clause #138 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_2)) % 32.44/32.66 (Or (Eq (in (skS.0 3 a a_1 a_2 a_3) a) True) % 32.44/32.66 (Or (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_1) True) (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_2) True))) % 32.44/32.66 Clause #139 (by clausification #[138]): ∀ (a a_1 a_2 a_3 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_2)) % 32.44/32.66 (Or (Eq (in (skS.0 3 a a_1 a_2 a_3) a) True) % 32.44/32.66 (Or (Eq (Eq (skS.0 3 a a_1 a_2 a_3) a_2) True) (Eq (skS.0 3 a a_1 a_2 a_3) a_1))) % 32.44/32.66 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 a_3 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_2)) % 32.44/32.66 (Or (Eq (in (skS.0 3 a a_1 a_2 a_3) a) True) (Or (Eq (skS.0 3 a a_1 a_2 a_3) a_1) (Eq (skS.0 3 a a_1 a_2 a_3) a_2))) % 32.44/32.66 Clause #156 (by equality factoring #[140]): ∀ (a a_1 a_2 a_3 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_2)) % 32.44/32.66 (Or (Eq (in (skS.0 3 a a_1 a_2 a_3) a) True) (Or (Ne a_1 a_2) (Eq (skS.0 3 a a_1 a_2 a_3) a_2))) % 32.44/32.66 Clause #9549 (by destructive equality resolution #[156]): ∀ (a a_1 a_2 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_1)) (Or (Eq (in (skS.0 3 a a_1 a_1 a_2) a) True) (Eq (skS.0 3 a a_1 a_1 a_2) a_1)) % 32.44/32.66 Clause #9610 (by superposition #[9549, 61]): ∀ (a a_1 a_2 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_1)) % 32.44/32.66 (Or (Eq (in (skS.0 3 a a_1 a_1 a_2) a) True) % 32.44/32.66 (Or (Eq a (unordered_pair a_1 a_1)) (Or (Eq (in a_1 a) False) (Ne a_1 a_1)))) % 32.44/32.66 Clause #9642 (by eliminate duplicate literals #[9610]): ∀ (a a_1 a_2 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_1)) % 32.44/32.66 (Or (Eq (in (skS.0 3 a a_1 a_1 a_2) a) True) (Or (Eq (in a_1 a) False) (Ne a_1 a_1))) % 32.44/32.66 Clause #9643 (by eliminate resolved literals #[9642]): ∀ (a a_1 a_2 : Iota), % 32.44/32.66 Or (Eq a (unordered_pair a_1 a_1)) (Or (Eq (in (skS.0 3 a a_1 a_1 a_2) a) True) (Eq (in a_1 a) False)) % 32.44/32.66 Clause #9666 (by superposition #[9643, 42]): ∀ (a a_1 : Iota), % 32.44/32.66 Or (Eq (singleton a) (unordered_pair a a)) % 32.44/32.66 (Or (Eq (in (skS.0 3 (singleton a) a a a_1) (singleton a)) True) (Eq False True)) % 32.44/32.66 Clause #9707 (by clausification #[9666]): ∀ (a a_1 : Iota), % 32.44/32.66 Or (Eq (singleton a) (unordered_pair a a)) (Eq (in (skS.0 3 (singleton a) a a a_1) (singleton a)) True) % 32.44/32.66 Clause #9708 (by superposition #[9707, 46]): ∀ (a a_1 : Iota), Or (Eq (singleton a) (unordered_pair a a)) (Or (Eq True False) (Eq (skS.0 3 (singleton a) a a a_1) a)) % 32.44/32.66 Clause #9812 (by clausification #[9708]): ∀ (a a_1 : Iota), Or (Eq (singleton a) (unordered_pair a a)) (Eq (skS.0 3 (singleton a) a a a_1) a) % 32.44/32.66 Clause #9813 (by superposition #[9812, 61]): ∀ (a : Iota), % 32.44/32.66 Or (Eq (singleton a) (unordered_pair a a)) % 32.44/32.66 (Or (Eq (singleton a) (unordered_pair a a)) (Or (Eq (in a (singleton a)) False) (Ne a a))) % 32.44/32.66 Clause #9857 (by eliminate duplicate literals #[9813]): ∀ (a : Iota), Or (Eq (singleton a) (unordered_pair a a)) (Or (Eq (in a (singleton a)) False) (Ne a a)) % 32.44/32.66 Clause #9858 (by eliminate resolved literals #[9857]): ∀ (a : Iota), Or (Eq (singleton a) (unordered_pair a a)) (Eq (in a (singleton a)) False) % 32.44/32.66 Clause #9859 (by forward demodulation #[9858, 42]): ∀ (a : Iota), Or (Eq (singleton a) (unordered_pair a a)) (Eq True False) % 32.44/32.66 Clause #9860 (by clausification #[9859]): ∀ (a : Iota), Eq (singleton a) (unordered_pair a a) % 32.44/32.66 Clause #9872 (by backward contextual literal cutting #[9860, 22]): False % 32.44/32.66 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------