%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU641^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:02:06 PM UTC 2025 % Result : Theorem 3.53s 3.76s % Output : Proof 3.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU641^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.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 05:31:53 EDT 2025 % 0.13/0.35 % CPUTime : % 3.53/3.76 SZS status Theorem for theBenchmark.p % 3.53/3.76 SZS output start Proof for theBenchmark.p % 3.53/3.76 Clause #0 (by assumption #[]): Eq (Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))) True % 3.53/3.76 Clause #1 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 3.53/3.76 Clause #2 (by assumption #[]): Eq (Not (setadjoinIL → uniqinunit → ∀ (Xx Xy : Iota), Eq (setadjoin Xx emptyset) (setadjoin Xy emptyset) → Eq Xx Xy)) % 3.53/3.76 True % 3.53/3.76 Clause #3 (by clausification #[2]): Eq (setadjoinIL → uniqinunit → ∀ (Xx Xy : Iota), Eq (setadjoin Xx emptyset) (setadjoin Xy emptyset) → Eq Xx Xy) False % 3.53/3.76 Clause #4 (by clausification #[3]): Eq setadjoinIL True % 3.53/3.76 Clause #5 (by clausification #[3]): Eq (uniqinunit → ∀ (Xx Xy : Iota), Eq (setadjoin Xx emptyset) (setadjoin Xy emptyset) → Eq Xx Xy) False % 3.53/3.76 Clause #6 (by clausification #[5]): Eq uniqinunit True % 3.53/3.76 Clause #7 (by clausification #[5]): Eq (∀ (Xx Xy : Iota), Eq (setadjoin Xx emptyset) (setadjoin Xy emptyset) → Eq Xx Xy) False % 3.53/3.76 Clause #8 (by clausification #[7]): ∀ (a : Iota), % 3.53/3.76 Eq (Not (∀ (Xy : Iota), Eq (setadjoin (skS.0 0 a) emptyset) (setadjoin Xy emptyset) → Eq (skS.0 0 a) Xy)) True % 3.53/3.76 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Eq (setadjoin (skS.0 0 a) emptyset) (setadjoin Xy emptyset) → Eq (skS.0 0 a) Xy) False % 3.53/3.76 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 3.53/3.76 Eq (Not (Eq (setadjoin (skS.0 0 a) emptyset) (setadjoin (skS.0 1 a a_1) emptyset) → Eq (skS.0 0 a) (skS.0 1 a a_1))) % 3.53/3.76 True % 3.53/3.76 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 3.53/3.76 Eq (Eq (setadjoin (skS.0 0 a) emptyset) (setadjoin (skS.0 1 a a_1) emptyset) → Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 3.53/3.76 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (Eq (setadjoin (skS.0 0 a) emptyset) (setadjoin (skS.0 1 a a_1) emptyset)) True % 3.53/3.76 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 3.53/3.76 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (setadjoin (skS.0 0 a) emptyset) (setadjoin (skS.0 1 a a_1) emptyset) % 3.53/3.76 Clause #15 (by clausification #[1]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.53/3.76 Clause #16 (by forward demodulation #[15, 6]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.53/3.76 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True % 3.53/3.76 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True % 3.53/3.76 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 3.53/3.76 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1) % 3.53/3.76 Clause #22 (by clausification #[0]): Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 3.53/3.76 Clause #23 (by forward demodulation #[22, 4]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 3.53/3.76 Clause #24 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin a Xy)) True % 3.53/3.76 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a a_1)) True % 3.53/3.76 Clause #26 (by superposition #[25, 14]): ∀ (a a_1 : Iota), Eq (in (skS.0 1 a a_1) (setadjoin (skS.0 0 a) emptyset)) True % 3.53/3.76 Clause #27 (by clausification #[13]): ∀ (a a_1 : Iota), Ne (skS.0 0 a) (skS.0 1 a a_1) % 3.53/3.76 Clause #28 (by superposition #[26, 20]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 3.53/3.76 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (skS.0 1 a a_1) (skS.0 0 a) % 3.53/3.76 Clause #30 (by forward contextual literal cutting #[29, 27]): False % 3.53/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------