%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET907+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:00:40 PM UTC 2025 % Result : Theorem 7.34s 7.56s % Output : Proof 7.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.10 % Problem : SET907+1 : TPTP v9.2.0. Released v3.2.0. % 0.09/0.11 % Command : duper %s % 0.11/0.32 % Computer : n019.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Thu Oct 2 13:58:08 EDT 2025 % 0.11/0.32 % CPUTime : % 7.34/7.56 SZS status Theorem for theBenchmark.p % 7.34/7.56 SZS output start Proof for theBenchmark.p % 7.34/7.56 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 7.34/7.56 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True % 7.34/7.56 Clause #9 (by assumption #[]): Eq (∀ (A B : Iota), subset A B → Eq (set_union2 A B) B) True % 7.34/7.56 Clause #10 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (subset (unordered_pair A B) C) (And (in A C) (in B C))) True % 7.34/7.56 Clause #11 (by assumption #[]): Eq (Not (∀ (A B C : Iota), And (in A B) (in C B) → Eq (set_union2 (unordered_pair A C) B) B)) True % 7.34/7.56 Clause #25 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 7.34/7.56 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 7.34/7.56 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 7.34/7.56 Clause #39 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a B → Eq (set_union2 a B) B) True % 7.34/7.56 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (subset a a_1 → Eq (set_union2 a a_1) a_1) True % 7.34/7.56 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (Eq (set_union2 a a_1) a_1) True) % 7.34/7.56 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_union2 a a_1) a_1) % 7.34/7.56 Clause #44 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True % 7.34/7.56 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True % 7.34/7.56 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a) % 7.34/7.56 Clause #47 (by clausification #[11]): Eq (∀ (A B C : Iota), And (in A B) (in C B) → Eq (set_union2 (unordered_pair A C) B) B) False % 7.34/7.56 Clause #48 (by clausification #[47]): ∀ (a : Iota), % 7.34/7.56 Eq (Not (∀ (B C : Iota), And (in (skS.0 2 a) B) (in C B) → Eq (set_union2 (unordered_pair (skS.0 2 a) C) B) B)) True % 7.34/7.56 Clause #49 (by clausification #[48]): ∀ (a : Iota), % 7.34/7.56 Eq (∀ (B C : Iota), And (in (skS.0 2 a) B) (in C B) → Eq (set_union2 (unordered_pair (skS.0 2 a) C) B) B) False % 7.34/7.56 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 7.34/7.56 Eq % 7.34/7.56 (Not % 7.34/7.56 (∀ (C : Iota), % 7.34/7.56 And (in (skS.0 2 a) (skS.0 3 a a_1)) (in C (skS.0 3 a a_1)) → % 7.34/7.56 Eq (set_union2 (unordered_pair (skS.0 2 a) C) (skS.0 3 a a_1)) (skS.0 3 a a_1))) % 7.34/7.56 True % 7.34/7.56 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), % 7.34/7.56 Eq % 7.34/7.56 (∀ (C : Iota), % 7.34/7.56 And (in (skS.0 2 a) (skS.0 3 a a_1)) (in C (skS.0 3 a a_1)) → % 7.34/7.56 Eq (set_union2 (unordered_pair (skS.0 2 a) C) (skS.0 3 a a_1)) (skS.0 3 a a_1)) % 7.34/7.56 False % 7.34/7.56 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 7.34/7.56 Eq % 7.34/7.56 (Not % 7.34/7.56 (And (in (skS.0 2 a) (skS.0 3 a a_1)) (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) → % 7.34/7.56 Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1))) % 7.34/7.56 True % 7.34/7.56 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 7.34/7.56 Eq % 7.34/7.56 (And (in (skS.0 2 a) (skS.0 3 a a_1)) (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) → % 7.34/7.56 Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1)) % 7.34/7.56 False % 7.34/7.56 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Eq (And (in (skS.0 2 a) (skS.0 3 a a_1)) (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1))) True % 7.34/7.56 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 7.34/7.56 Eq (Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1)) False % 7.34/7.56 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 a a_1 a_2) (skS.0 3 a a_1)) True % 7.34/7.56 Clause #57 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True % 7.34/7.56 Clause #60 (by clausification #[10]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (subset (unordered_pair a B) C) (And (in a C) (in B C))) True % 7.34/7.56 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Iff (subset (unordered_pair a a_1) C) (And (in a C) (in a_1 C))) True % 7.34/7.59 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), Eq (Iff (subset (unordered_pair a a_1) a_2) (And (in a a_2) (in a_1 a_2))) True % 7.34/7.59 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) True) (Eq (And (in a a_2) (in a_1 a_2)) False) % 7.34/7.59 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 7.34/7.59 Or (Eq (subset (unordered_pair a a_1) a_2) True) (Or (Eq (in a a_2) False) (Eq (in a_1 a_2) False)) % 7.34/7.59 Clause #66 (by superposition #[65, 56]): ∀ (a a_1 a_2 a_3 : Iota), % 7.34/7.59 Or (Eq (subset (unordered_pair (skS.0 4 a a_1 a_2) a_3) (skS.0 3 a a_1)) True) % 7.34/7.59 (Or (Eq (in a_3 (skS.0 3 a a_1)) False) (Eq False True)) % 7.34/7.59 Clause #75 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Ne (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1) % 7.34/7.59 Clause #76 (by forward demodulation #[75, 46]): ∀ (a a_1 a_2 : Iota), Ne (set_union2 (skS.0 3 a a_1) (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))) (skS.0 3 a a_1) % 7.34/7.59 Clause #103 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 7.34/7.59 Or (Eq (subset (unordered_pair (skS.0 4 a a_1 a_2) a_3) (skS.0 3 a a_1)) True) (Eq (in a_3 (skS.0 3 a a_1)) False) % 7.34/7.59 Clause #105 (by superposition #[103, 57]): ∀ (a a_1 a_2 : Iota), % 7.34/7.59 Or (Eq (subset (unordered_pair (skS.0 4 a a_1 a_2) (skS.0 2 a)) (skS.0 3 a a_1)) True) (Eq False True) % 7.34/7.59 Clause #128 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 4 a a_1 a_2) (skS.0 2 a)) (skS.0 3 a a_1)) True % 7.34/7.59 Clause #129 (by forward demodulation #[128, 27]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) True % 7.34/7.59 Clause #130 (by superposition #[129, 42]): ∀ (a a_1 a_2 : Iota), % 7.34/7.59 Or (Eq True False) (Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1)) % 7.34/7.59 Clause #141 (by clausification #[130]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2)) (skS.0 3 a a_1)) (skS.0 3 a a_1) % 7.34/7.59 Clause #144 (by superposition #[141, 46]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 (skS.0 3 a a_1) (unordered_pair (skS.0 2 a) (skS.0 4 a a_1 a_2))) (skS.0 3 a a_1) % 7.34/7.59 Clause #145 (by forward contextual literal cutting #[144, 76]): False % 7.34/7.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------