%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SWW469+1 : TPTP v9.2.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 08:06:12 PM UTC 2025 % Result : Theorem 3.34s 3.58s % Output : Proof 3.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SWW469+1 : TPTP v9.2.0. Released v5.3.0. % 0.10/0.11 % Command : duper %s % 0.10/0.31 % Computer : n025.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Thu Oct 2 11:03:53 EDT 2025 % 0.10/0.31 % CPUTime : % 3.34/3.58 SZS status Theorem for theBenchmark.p % 3.34/3.58 SZS output start Proof for theBenchmark.p % 3.34/3.58 Clause #0 (by assumption #[]): Eq (is_state (undefined_state state)) True % 3.34/3.58 Clause #1 (by assumption #[]): Eq (Iff hoare_165779456gleton (Exists fun S => Exists fun T => And (And (is_state S) (is_state T)) (Ne S T))) True % 3.34/3.58 Clause #4 (by assumption #[]): Eq hoare_165779456gleton True % 3.34/3.58 Clause #5 (by assumption #[]): Eq (Not (∀ (T : Iota), is_state T → Not (∀ (S : Iota), is_state S → Eq S T))) True % 3.34/3.58 Clause #7 (by clausification #[5]): Eq (∀ (T : Iota), is_state T → Not (∀ (S : Iota), is_state S → Eq S T)) False % 3.34/3.58 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (is_state (skS.0 0 a) → Not (∀ (S : Iota), is_state S → Eq S (skS.0 0 a)))) True % 3.34/3.58 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (is_state (skS.0 0 a) → Not (∀ (S : Iota), is_state S → Eq S (skS.0 0 a))) False % 3.34/3.58 Clause #11 (by clausification #[9]): ∀ (a : Iota), Eq (Not (∀ (S : Iota), is_state S → Eq S (skS.0 0 a))) False % 3.34/3.58 Clause #13 (by clausification #[1]): Or (Eq hoare_165779456gleton False) % 3.34/3.58 (Eq (Exists fun S => Exists fun T => And (And (is_state S) (is_state T)) (Ne S T)) True) % 3.34/3.58 Clause #20 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (S : Iota), is_state S → Eq S (skS.0 0 a)) True % 3.34/3.58 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (is_state a → Eq a (skS.0 0 a_1)) True % 3.34/3.58 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (is_state a) False) (Eq (Eq a (skS.0 0 a_1)) True) % 3.34/3.58 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (is_state a) False) (Eq a (skS.0 0 a_1)) % 3.34/3.58 Clause #24 (by superposition #[23, 0]): ∀ (a : Iota), Or (Eq (undefined_state state) (skS.0 0 a)) (Eq False True) % 3.34/3.58 Clause #26 (by clausification #[24]): ∀ (a : Iota), Eq (undefined_state state) (skS.0 0 a) % 3.34/3.58 Clause #27 (by backward demodulation #[26, 23]): ∀ (a : Iota), Or (Eq (is_state a) False) (Eq a (undefined_state state)) % 3.34/3.58 Clause #31 (by clausification #[13]): ∀ (a : Iota), % 3.34/3.58 Or (Eq hoare_165779456gleton False) % 3.34/3.58 (Eq (Exists fun T => And (And (is_state (skS.0 1 a)) (is_state T)) (Ne (skS.0 1 a) T)) True) % 3.34/3.58 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 3.34/3.58 Or (Eq hoare_165779456gleton False) % 3.34/3.58 (Eq (And (And (is_state (skS.0 1 a)) (is_state (skS.0 2 a a_1))) (Ne (skS.0 1 a) (skS.0 2 a a_1))) True) % 3.34/3.58 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq hoare_165779456gleton False) (Eq (Ne (skS.0 1 a) (skS.0 2 a a_1)) True) % 3.34/3.58 Clause #34 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq hoare_165779456gleton False) (Eq (And (is_state (skS.0 1 a)) (is_state (skS.0 2 a a_1))) True) % 3.34/3.58 Clause #35 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq hoare_165779456gleton False) (Ne (skS.0 1 a) (skS.0 2 a a_1)) % 3.34/3.58 Clause #36 (by forward demodulation #[35, 4]): ∀ (a a_1 : Iota), Or (Eq True False) (Ne (skS.0 1 a) (skS.0 2 a a_1)) % 3.34/3.58 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Ne (skS.0 1 a) (skS.0 2 a a_1) % 3.34/3.58 Clause #38 (by clausification #[34]): ∀ (a a_1 : Iota), Or (Eq hoare_165779456gleton False) (Eq (is_state (skS.0 2 a a_1)) True) % 3.34/3.58 Clause #39 (by clausification #[34]): ∀ (a : Iota), Or (Eq hoare_165779456gleton False) (Eq (is_state (skS.0 1 a)) True) % 3.34/3.58 Clause #40 (by forward demodulation #[38, 4]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (is_state (skS.0 2 a a_1)) True) % 3.34/3.58 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (is_state (skS.0 2 a a_1)) True % 3.34/3.58 Clause #42 (by superposition #[41, 27]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 a a_1) (undefined_state state)) % 3.34/3.58 Clause #43 (by forward demodulation #[39, 4]): ∀ (a : Iota), Or (Eq True False) (Eq (is_state (skS.0 1 a)) True) % 3.34/3.58 Clause #44 (by clausification #[43]): ∀ (a : Iota), Eq (is_state (skS.0 1 a)) True % 3.34/3.58 Clause #45 (by superposition #[44, 27]): ∀ (a : Iota), Or (Eq True False) (Eq (skS.0 1 a) (undefined_state state)) % 3.34/3.58 Clause #46 (by clausification #[45]): ∀ (a : Iota), Eq (skS.0 1 a) (undefined_state state) % 3.34/3.58 Clause #47 (by backward demodulation #[46, 37]): ∀ (a a_1 : Iota), Ne (undefined_state state) (skS.0 2 a a_1) % 3.34/3.58 Clause #48 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (skS.0 2 a a_1) (undefined_state state) % 3.34/3.58 Clause #49 (by forward contextual literal cutting #[48, 47]): False % 3.34/3.58 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------