%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU663^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:02:10 PM UTC 2025 % Result : Theorem 3.58s 3.73s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU663^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 04:40:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.58/3.73 SZS status Theorem for theBenchmark.p % 3.58/3.73 SZS output start Proof for theBenchmark.p % 3.58/3.73 Clause #0 (by assumption #[]): Eq (Eq ksndpairEq (∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy)) True % 3.58/3.73 Clause #2 (by assumption #[]): Eq % 3.58/3.73 (Not % 3.58/3.73 (ksndpairEq → % 3.58/3.73 cartprodmempaircEq → ∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy)) % 3.58/3.73 True % 3.58/3.73 Clause #3 (by clausification #[0]): Eq ksndpairEq (∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy) % 3.58/3.73 Clause #5 (by clausify Prop equality #[3]): Or (Eq ksndpairEq False) (Eq (∀ (Xx Xy : Iota), Eq (ksnd (kpair Xx Xy)) Xy) True) % 3.58/3.73 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq ksndpairEq False) (Eq (∀ (Xy : Iota), Eq (ksnd (kpair a Xy)) Xy) True) % 3.58/3.73 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq ksndpairEq False) (Eq (Eq (ksnd (kpair a a_1)) a_1) True) % 3.58/3.73 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq ksndpairEq False) (Eq (ksnd (kpair a a_1)) a_1) % 3.58/3.73 Clause #15 (by clausification #[2]): Eq (ksndpairEq → cartprodmempaircEq → ∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy) % 3.58/3.73 False % 3.58/3.73 Clause #16 (by clausification #[15]): Eq ksndpairEq True % 3.58/3.73 Clause #17 (by clausification #[15]): Eq (cartprodmempaircEq → ∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy) False % 3.58/3.73 Clause #20 (by superposition #[16, 9]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ksnd (kpair a a_1)) a_1) % 3.58/3.73 Clause #25 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (ksnd (kpair a a_1)) a_1 % 3.58/3.73 Clause #29 (by clausification #[17]): Eq (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy) False % 3.58/3.73 Clause #31 (by clausification #[29]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), in Xx (skS.0 2 a) → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy)) True % 3.58/3.73 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (skS.0 2 a) → ∀ (Xy : Iota), in Xy B → Eq (ksnd (kpair Xx Xy)) Xy) False % 3.58/3.73 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), % 3.58/3.73 Eq (Not (∀ (Xx : Iota), in Xx (skS.0 2 a) → ∀ (Xy : Iota), in Xy (skS.0 3 a a_1) → Eq (ksnd (kpair Xx Xy)) Xy)) True % 3.58/3.73 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 3.58/3.73 Eq (∀ (Xx : Iota), in Xx (skS.0 2 a) → ∀ (Xy : Iota), in Xy (skS.0 3 a a_1) → Eq (ksnd (kpair Xx Xy)) Xy) False % 3.58/3.73 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 3.58/3.73 Eq % 3.58/3.73 (Not % 3.58/3.73 (in (skS.0 4 a a_1 a_2) (skS.0 2 a) → % 3.58/3.73 ∀ (Xy : Iota), in Xy (skS.0 3 a a_1) → Eq (ksnd (kpair (skS.0 4 a a_1 a_2) Xy)) Xy)) % 3.58/3.73 True % 3.58/3.73 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 3.58/3.73 Eq % 3.58/3.73 (in (skS.0 4 a a_1 a_2) (skS.0 2 a) → % 3.58/3.73 ∀ (Xy : Iota), in Xy (skS.0 3 a a_1) → Eq (ksnd (kpair (skS.0 4 a a_1 a_2) Xy)) Xy) % 3.58/3.73 False % 3.58/3.73 Clause #38 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xy : Iota), in Xy (skS.0 3 a a_1) → Eq (ksnd (kpair (skS.0 4 a a_1 a_2) Xy)) Xy) False % 3.58/3.73 Clause #62 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.73 Eq % 3.58/3.73 (Not % 3.58/3.73 (in (skS.0 8 a a_1 a_2 a_3) (skS.0 3 a a_1) → % 3.58/3.73 Eq (ksnd (kpair (skS.0 4 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3))) (skS.0 8 a a_1 a_2 a_3))) % 3.58/3.73 True % 3.58/3.73 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.73 Eq % 3.58/3.73 (in (skS.0 8 a a_1 a_2 a_3) (skS.0 3 a a_1) → % 3.58/3.73 Eq (ksnd (kpair (skS.0 4 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3))) (skS.0 8 a a_1 a_2 a_3)) % 3.58/3.73 False % 3.58/3.73 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 a_3 : Iota), % 3.58/3.73 Eq (Eq (ksnd (kpair (skS.0 4 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3))) (skS.0 8 a a_1 a_2 a_3)) False % 3.58/3.73 Clause #71 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), Ne (ksnd (kpair (skS.0 4 a a_1 a_2) (skS.0 8 a a_1 a_2 a_3))) (skS.0 8 a a_1 a_2 a_3) % 3.58/3.73 Clause #72 (by forward demodulation #[71, 25]): ∀ (a a_1 a_2 a_3 : Iota), Ne (skS.0 8 a a_1 a_2 a_3) (skS.0 8 a a_1 a_2 a_3) % 3.58/3.73 Clause #73 (by eliminate resolved literals #[72]): False % 3.58/3.73 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------