%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU230+2 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:01:11 PM UTC 2025 % Result : Theorem 205.01s 205.24s % Output : Proof 205.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU230+2 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n013.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 06:42:08 EDT 2025 % 0.14/0.35 % CPUTime : % 205.01/205.24 SZS status Theorem for theBenchmark.p % 205.01/205.24 SZS output start Proof for theBenchmark.p % 205.01/205.24 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True % 205.01/205.24 Clause #17 (by assumption #[]): Eq (∀ (A : Iota), Eq (succ A) (set_union2 A (singleton A))) True % 205.01/205.24 Clause #97 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset (singleton A) B) (in A B)) True % 205.01/205.24 Clause #122 (by assumption #[]): Eq (Not (∀ (A : Iota), in A (succ A))) True % 205.01/205.24 Clause #216 (by assumption #[]): Eq (∀ (A B : Iota), subset A (set_union2 A B)) True % 205.01/205.24 Clause #305 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True % 205.01/205.24 Clause #306 (by clausification #[305]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True % 205.01/205.24 Clause #307 (by clausification #[306]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a) % 205.01/205.24 Clause #331 (by clausification #[122]): Eq (∀ (A : Iota), in A (succ A)) False % 205.01/205.24 Clause #332 (by clausification #[331]): ∀ (a : Iota), Eq (Not (in (skS.0 2 a) (succ (skS.0 2 a)))) True % 205.01/205.24 Clause #333 (by clausification #[332]): ∀ (a : Iota), Eq (in (skS.0 2 a) (succ (skS.0 2 a))) False % 205.01/205.24 Clause #715 (by clausification #[216]): ∀ (a : Iota), Eq (∀ (B : Iota), subset a (set_union2 a B)) True % 205.01/205.24 Clause #716 (by clausification #[715]): ∀ (a a_1 : Iota), Eq (subset a (set_union2 a a_1)) True % 205.01/205.24 Clause #719 (by superposition #[716, 307]): ∀ (a a_1 : Iota), Eq (subset a (set_union2 a_1 a)) True % 205.01/205.24 Clause #831 (by clausification #[17]): ∀ (a : Iota), Eq (Eq (succ a) (set_union2 a (singleton a))) True % 205.01/205.24 Clause #832 (by clausification #[831]): ∀ (a : Iota), Eq (succ a) (set_union2 a (singleton a)) % 205.01/205.24 Clause #834 (by superposition #[832, 719]): ∀ (a : Iota), Eq (subset (singleton a) (succ a)) True % 205.01/205.24 Clause #2639 (by clausification #[97]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset (singleton a) B) (in a B)) True % 205.01/205.24 Clause #2640 (by clausification #[2639]): ∀ (a a_1 : Iota), Eq (Iff (subset (singleton a) a_1) (in a a_1)) True % 205.01/205.24 Clause #2642 (by clausification #[2640]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) a_1) False) (Eq (in a a_1) True) % 205.01/205.24 Clause #10600 (by superposition #[2642, 834]): ∀ (a : Iota), Or (Eq (in a (succ a)) True) (Eq False True) % 205.01/205.24 Clause #10612 (by clausification #[10600]): ∀ (a : Iota), Eq (in a (succ a)) True % 205.01/205.24 Clause #10613 (by superposition #[10612, 333]): Eq True False % 205.01/205.24 Clause #10628 (by clausification #[10613]): False % 205.01/205.24 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------