%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU514^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:01:47 PM UTC 2025 % Result : Theorem 3.58s 3.76s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.11 % Problem : SEU514^2 : TPTP v9.2.0. Released v3.7.0. % 0.02/0.13 % Command : duper %s % 0.13/0.34 % Computer : n014.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 06:13:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.58/3.76 SZS status Theorem for theBenchmark.p % 3.58/3.76 SZS output start Proof for theBenchmark.p % 3.58/3.76 Clause #0 (by assumption #[]): Eq (Eq setadjoinAx (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A)))) True % 3.58/3.76 Clause #1 (by assumption #[]): Eq (Not (setadjoinAx → ∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A))) True % 3.58/3.76 Clause #2 (by clausification #[1]): Eq (setadjoinAx → ∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A)) False % 3.58/3.76 Clause #3 (by clausification #[2]): Eq setadjoinAx True % 3.58/3.76 Clause #4 (by clausification #[2]): Eq (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A)) False % 3.58/3.76 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (A Xy : Iota), in Xy A → in Xy (setadjoin (skS.0 0 a) A))) True % 3.58/3.76 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (A Xy : Iota), in Xy A → in Xy (setadjoin (skS.0 0 a) A)) False % 3.58/3.76 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Not (∀ (Xy : Iota), in Xy (skS.0 1 a a_1) → in Xy (setadjoin (skS.0 0 a) (skS.0 1 a a_1)))) True % 3.58/3.76 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (∀ (Xy : Iota), in Xy (skS.0 1 a a_1) → in Xy (setadjoin (skS.0 0 a) (skS.0 1 a a_1))) False % 3.58/3.76 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.58/3.76 Eq (Not (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1)))) % 3.58/3.76 True % 3.58/3.76 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.58/3.76 Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1) → in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1))) False % 3.58/3.76 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a a_1)) True % 3.58/3.76 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a a_1 a_2) (setadjoin (skS.0 0 a) (skS.0 1 a a_1))) False % 3.58/3.76 Clause #13 (by clausification #[0]): Eq setadjoinAx (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A))) % 3.58/3.76 Clause #14 (by forward demodulation #[13, 3]): Eq True (∀ (Xx A Xy : Iota), Iff (in Xy (setadjoin Xx A)) (Or (Eq Xy Xx) (in Xy A))) % 3.58/3.76 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (A Xy : Iota), Iff (in Xy (setadjoin a A)) (Or (Eq Xy a) (in Xy A))) True % 3.58/3.76 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (∀ (Xy : Iota), Iff (in Xy (setadjoin a a_1)) (Or (Eq Xy a) (in Xy a_1))) True % 3.58/3.76 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Eq (Iff (in a (setadjoin a_1 a_2)) (Or (Eq a a_1) (in a a_2))) True % 3.58/3.76 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) True) (Eq (Or (Eq a a_1) (in a a_2)) False) % 3.58/3.76 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 a_2)) True) (Eq (in a a_2) False) % 3.58/3.76 Clause #22 (by superposition #[20, 11]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) (setadjoin a_3 (skS.0 1 a a_1))) True) (Eq False True) % 3.58/3.76 Clause #40 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 2 a a_1 a_2) (setadjoin a_3 (skS.0 1 a a_1))) True % 3.58/3.76 Clause #41 (by superposition #[40, 12]): Eq True False % 3.58/3.76 Clause #44 (by clausification #[41]): False % 3.58/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------