%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO353^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 08:08:55 PM UTC 2025 % Result : Theorem 3.62s 3.80s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SYO353^5 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.14 % Command : duper %s % 0.13/0.35 % Computer : n027.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 14:09:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.62/3.80 SZS status Theorem for theBenchmark.p % 3.62/3.80 SZS output start Proof for theBenchmark.p % 3.62/3.80 Clause #0 (by assumption #[]): Eq (Not ((∀ (Xq : a → Prop), Xq u → Xq v) → ∀ (Q : a → a → Prop), (∀ (Z : a), Q Z Z) → Q u v)) True % 3.62/3.80 Clause #1 (by clausification #[0]): Eq ((∀ (Xq : a → Prop), Xq u → Xq v) → ∀ (Q : a → a → Prop), (∀ (Z : a), Q Z Z) → Q u v) False % 3.62/3.80 Clause #2 (by clausification #[1]): Eq (∀ (Xq : a → Prop), Xq u → Xq v) True % 3.62/3.80 Clause #3 (by clausification #[1]): Eq (∀ (Q : a → a → Prop), (∀ (Z : a), Q Z Z) → Q u v) False % 3.62/3.80 Clause #4 (by clausification #[2]): ∀ (a : a → Prop), Eq (a u → a v) True % 3.62/3.80 Clause #5 (by clausification #[4]): ∀ (a : a → Prop), Or (Eq (a u) False) (Eq (a v) True) % 3.62/3.80 Clause #7 (by neHoist #[5]): ∀ (a_1 : a → Sort _abstMVar.0) (a_2 a_3 : (x : a) → a_1 x), % 3.62/3.80 Or (Eq ((fun x => Ne (a_2 x) (a_3 x)) v) True) (Or (Eq True False) (Eq (a_2 u) (a_3 u))) % 3.62/3.80 Clause #14 (by clausification #[3]): ∀ (a_1 : a → a → Prop), Eq (Not ((∀ (Z : a), skS.0 0 a_1 Z Z) → skS.0 0 a_1 u v)) True % 3.62/3.80 Clause #15 (by clausification #[14]): ∀ (a_1 : a → a → Prop), Eq ((∀ (Z : a), skS.0 0 a_1 Z Z) → skS.0 0 a_1 u v) False % 3.62/3.80 Clause #16 (by clausification #[15]): ∀ (a_1 : a → a → Prop), Eq (∀ (Z : a), skS.0 0 a_1 Z Z) True % 3.62/3.80 Clause #17 (by clausification #[15]): ∀ (a_1 : a → a → Prop), Eq (skS.0 0 a_1 u v) False % 3.62/3.80 Clause #18 (by clausification #[16]): ∀ (a_1 : a → a → Prop) (a_2 : a), Eq (skS.0 0 a_1 a_2 a_2) True % 3.62/3.80 Clause #31 (by betaEtaReduce #[7]): ∀ (a_1 : a → Sort _abstMVar.0) (a_2 a : (x : a) → a_1 x), % 3.62/3.80 Or (Eq (Ne (a_2 v) (a v)) True) (Or (Eq True False) (Eq (a_2 u) (a u))) % 3.62/3.80 Clause #32 (by clausification #[31]): ∀ (a_1 : a → Sort _abstMVar.0) (a_2 a : (x : a) → a_1 x), Or (Eq True False) (Or (Eq (a_2 u) (a u)) (Ne (a_2 v) (a v))) % 3.62/3.80 Clause #33 (by clausification #[32]): ∀ (a_1 : a → Sort _abstMVar.0) (a_2 a : (x : a) → a_1 x), Or (Eq (a_2 u) (a u)) (Ne (a_2 v) (a v)) % 3.62/3.80 Clause #34 (by equality resolution #[33]): Eq ((fun x => x) u) ((fun x => v) u) % 3.62/3.80 Clause #41 (by betaEtaReduce #[34]): Eq u v % 3.62/3.80 Clause #44 (by backward demodulation #[41, 17]): ∀ (a_1 : a → a → Prop), Eq (skS.0 0 a_1 u u) False % 3.62/3.80 Clause #78 (by superposition #[44, 18]): Eq False True % 3.62/3.80 Clause #82 (by clausification #[78]): False % 3.62/3.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------