%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO358^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:08:56 PM UTC 2025 % Result : Theorem 3.86s 4.05s % Output : Proof 3.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO358^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n013.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 13:29:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.86/4.05 SZS status Theorem for theBenchmark.p % 3.86/4.05 SZS output start Proof for theBenchmark.p % 3.86/4.05 Clause #0 (by assumption #[]): Eq % 3.86/4.05 (Not % 3.86/4.05 ((∀ (Xq : atype → Prop), Xq u → Xq v) → ∀ (P : atype → Prop), And (Or a (Not a)) (P u) → And (Or b (Not b)) (P v))) % 3.86/4.05 True % 3.86/4.05 Clause #1 (by clausification #[0]): Eq ((∀ (Xq : atype → Prop), Xq u → Xq v) → ∀ (P : atype → Prop), And (Or a (Not a)) (P u) → And (Or b (Not b)) (P v)) % 3.86/4.05 False % 3.86/4.05 Clause #2 (by clausification #[1]): Eq (∀ (Xq : atype → Prop), Xq u → Xq v) True % 3.86/4.05 Clause #3 (by clausification #[1]): Eq (∀ (P : atype → Prop), And (Or a (Not a)) (P u) → And (Or b (Not b)) (P v)) False % 3.86/4.05 Clause #4 (by clausification #[2]): ∀ (a : atype → Prop), Eq (a u → a v) True % 3.86/4.05 Clause #5 (by clausification #[4]): ∀ (a : atype → Prop), Or (Eq (a u) False) (Eq (a v) True) % 3.86/4.05 Clause #7 (by neHoist #[5]): ∀ (a : atype → Sort _abstMVar.0) (a_1 a_2 : (x : atype) → a x), % 3.86/4.05 Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) v) True) (Or (Eq True False) (Eq (a_1 u) (a_2 u))) % 3.86/4.05 Clause #18 (by clausification #[3]): ∀ (a_1 : atype → Prop), Eq (Not (And (Or a (Not a)) (skS.0 0 a_1 u) → And (Or b (Not b)) (skS.0 0 a_1 v))) True % 3.86/4.05 Clause #19 (by clausification #[18]): ∀ (a_1 : atype → Prop), Eq (And (Or a (Not a)) (skS.0 0 a_1 u) → And (Or b (Not b)) (skS.0 0 a_1 v)) False % 3.86/4.05 Clause #20 (by clausification #[19]): ∀ (a_1 : atype → Prop), Eq (And (Or a (Not a)) (skS.0 0 a_1 u)) True % 3.86/4.05 Clause #21 (by clausification #[19]): ∀ (a : atype → Prop), Eq (And (Or b (Not b)) (skS.0 0 a v)) False % 3.86/4.05 Clause #22 (by clausification #[20]): ∀ (a : atype → Prop), Eq (skS.0 0 a u) True % 3.86/4.05 Clause #36 (by betaEtaReduce #[7]): ∀ (a : atype → Sort _abstMVar.0) (a_1 a_2 : (x : atype) → a x), % 3.86/4.05 Or (Eq (Ne (a_1 v) (a_2 v)) True) (Or (Eq True False) (Eq (a_1 u) (a_2 u))) % 3.86/4.05 Clause #37 (by clausification #[36]): ∀ (a : atype → Sort _abstMVar.0) (a_1 a_2 : (x : atype) → a x), % 3.86/4.05 Or (Eq True False) (Or (Eq (a_1 u) (a_2 u)) (Ne (a_1 v) (a_2 v))) % 3.86/4.05 Clause #38 (by clausification #[37]): ∀ (a : atype → Sort _abstMVar.0) (a_1 a_2 : (x : atype) → a x), Or (Eq (a_1 u) (a_2 u)) (Ne (a_1 v) (a_2 v)) % 3.86/4.05 Clause #39 (by equality resolution #[38]): Eq ((fun x => x) u) ((fun x => v) u) % 3.86/4.05 Clause #47 (by betaEtaReduce #[39]): Eq u v % 3.86/4.05 Clause #215 (by clausification #[21]): ∀ (a : atype → Prop), Or (Eq (Or b (Not b)) False) (Eq (skS.0 0 a v) False) % 3.86/4.05 Clause #216 (by clausification #[215]): ∀ (a : atype → Prop), Or (Eq (skS.0 0 a v) False) (Eq (Not b) False) % 3.86/4.05 Clause #217 (by clausification #[215]): ∀ (a : atype → Prop), Or (Eq (skS.0 0 a v) False) (Eq b False) % 3.86/4.05 Clause #218 (by clausification #[216]): ∀ (a : atype → Prop), Or (Eq (skS.0 0 a v) False) (Eq b True) % 3.86/4.05 Clause #219 (by forward demodulation #[218, 47]): ∀ (a : atype → Prop), Or (Eq (skS.0 0 a u) False) (Eq b True) % 3.86/4.05 Clause #220 (by superposition #[219, 22]): Or (Eq b True) (Eq False True) % 3.86/4.05 Clause #236 (by clausification #[220]): Eq b True % 3.86/4.05 Clause #254 (by forward demodulation #[217, 47]): ∀ (a : atype → Prop), Or (Eq (skS.0 0 a u) False) (Eq b False) % 3.86/4.05 Clause #255 (by forward demodulation #[254, 236]): ∀ (a : atype → Prop), Or (Eq (skS.0 0 a u) False) (Eq True False) % 3.86/4.05 Clause #256 (by clausification #[255]): ∀ (a : atype → Prop), Eq (skS.0 0 a u) False % 3.86/4.05 Clause #257 (by superposition #[256, 22]): Eq False True % 3.86/4.05 Clause #274 (by clausification #[257]): False % 3.86/4.05 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------