%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO359^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 4.79s 4.97s % Output : Proof 4.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYO359^5 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n018.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 14:30:53 EDT 2025 % 0.13/0.34 % CPUTime : % 4.79/4.97 SZS status Theorem for theBenchmark.p % 4.79/4.97 SZS output start Proof for theBenchmark.p % 4.79/4.97 Clause #0 (by assumption #[]): Eq % 4.79/4.97 (Not % 4.79/4.97 (((∀ (Xx : b), Iff (f Xx) (g Xx)) → ∀ (Xq : (b → Prop) → Prop), Xq f → Xq g) → % 4.79/4.97 (∀ (Xx : b), Iff (f Xx) (g Xx)) → Eq (h f) (h g))) % 4.79/4.97 True % 4.79/4.97 Clause #1 (by clausification #[0]): Eq % 4.79/4.97 (((∀ (Xx : b), Iff (f Xx) (g Xx)) → ∀ (Xq : (b → Prop) → Prop), Xq f → Xq g) → % 4.79/4.97 (∀ (Xx : b), Iff (f Xx) (g Xx)) → Eq (h f) (h g)) % 4.79/4.97 False % 4.79/4.97 Clause #2 (by clausification #[1]): Eq ((∀ (Xx : b), Iff (f Xx) (g Xx)) → ∀ (Xq : (b → Prop) → Prop), Xq f → Xq g) True % 4.79/4.97 Clause #3 (by clausification #[1]): Eq ((∀ (Xx : b), Iff (f Xx) (g Xx)) → Eq (h f) (h g)) False % 4.79/4.97 Clause #4 (by clausification #[2]): Or (Eq (∀ (Xx : b), Iff (f Xx) (g Xx)) False) (Eq (∀ (Xq : (b → Prop) → Prop), Xq f → Xq g) True) % 4.79/4.97 Clause #5 (by clausification #[4]): ∀ (a : b), Or (Eq (∀ (Xq : (b → Prop) → Prop), Xq f → Xq g) True) (Eq (Not (Iff (f (skS.0 0 a)) (g (skS.0 0 a)))) True) % 4.79/4.97 Clause #6 (by clausification #[5]): ∀ (a : b) (a_1 : (b → Prop) → Prop), Or (Eq (Not (Iff (f (skS.0 0 a)) (g (skS.0 0 a)))) True) (Eq (a_1 f → a_1 g) True) % 4.79/4.97 Clause #7 (by clausification #[6]): ∀ (a : (b → Prop) → Prop) (a_1 : b), Or (Eq (a f → a g) True) (Eq (Iff (f (skS.0 0 a_1)) (g (skS.0 0 a_1))) False) % 4.79/4.97 Clause #8 (by clausification #[7]): ∀ (a : b) (a_1 : (b → Prop) → Prop), % 4.79/4.97 Or (Eq (Iff (f (skS.0 0 a)) (g (skS.0 0 a))) False) (Or (Eq (a_1 f) False) (Eq (a_1 g) True)) % 4.79/4.97 Clause #9 (by clausification #[8]): ∀ (a : (b → Prop) → Prop) (a_1 : b), % 4.79/4.97 Or (Eq (a f) False) (Or (Eq (a g) True) (Or (Eq (f (skS.0 0 a_1)) False) (Eq (g (skS.0 0 a_1)) False))) % 4.79/4.97 Clause #10 (by clausification #[8]): ∀ (a : (b → Prop) → Prop) (a_1 : b), % 4.79/4.97 Or (Eq (a f) False) (Or (Eq (a g) True) (Or (Eq (f (skS.0 0 a_1)) True) (Eq (g (skS.0 0 a_1)) True))) % 4.79/4.97 Clause #16 (by fluidLoobHoist #[9]): ∀ (a : (b → Prop) → Prop) (a_1 : b), % 4.79/4.97 Or (Eq (a g) True) % 4.79/4.97 (Or (Eq (f (skS.0 0 a_1)) False) (Or (Eq (g (skS.0 0 a_1)) False) (Or (Eq True False) (Eq (a f) False)))) % 4.79/4.97 Clause #19 (by clausification #[3]): Eq (∀ (Xx : b), Iff (f Xx) (g Xx)) True % 4.79/4.97 Clause #20 (by clausification #[3]): Eq (Eq (h f) (h g)) False % 4.79/4.97 Clause #21 (by clausification #[19]): ∀ (a : b), Eq (Iff (f a) (g a)) True % 4.79/4.97 Clause #22 (by clausification #[21]): ∀ (a : b), Or (Eq (f a) True) (Eq (g a) False) % 4.79/4.97 Clause #23 (by clausification #[21]): ∀ (a : b), Or (Eq (f a) False) (Eq (g a) True) % 4.79/4.97 Clause #29 (by clausification #[20]): Ne (h f) (h g) % 4.79/4.97 Clause #35 (by neHoist #[10]): ∀ (a : (b → Prop) → Sort _abstMVar.0) (a_1 a_2 : (x : b → Prop) → a x) (a_3 : b), % 4.79/4.97 Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) g) True) % 4.79/4.97 (Or (Eq (f (skS.0 0 a_3)) True) (Or (Eq (g (skS.0 0 a_3)) True) (Or (Eq True False) (Eq (a_1 f) (a_2 f))))) % 4.79/4.97 Clause #52 (by clausification #[16]): ∀ (a : (b → Prop) → Prop) (a_1 : b), % 4.79/4.97 Or (Eq (a g) True) (Or (Eq (f (skS.0 0 a_1)) False) (Or (Eq (g (skS.0 0 a_1)) False) (Eq (a f) False))) % 4.79/4.97 Clause #98 (by betaEtaReduce #[35]): ∀ (a : (b → Prop) → Sort _abstMVar.0) (a_1 a_2 : (x : b → Prop) → a x) (a_3 : b), % 4.79/4.97 Or (Eq (Ne (a_1 g) (a_2 g)) True) % 4.79/4.97 (Or (Eq (f (skS.0 0 a_3)) True) (Or (Eq (g (skS.0 0 a_3)) True) (Or (Eq True False) (Eq (a_1 f) (a_2 f))))) % 4.79/4.97 Clause #99 (by clausification #[98]): ∀ (a : b) (a_1 : (b → Prop) → Sort _abstMVar.0) (a_2 a_3 : (x : b → Prop) → a_1 x), % 4.79/4.97 Or (Eq (f (skS.0 0 a)) True) % 4.79/4.97 (Or (Eq (g (skS.0 0 a)) True) (Or (Eq True False) (Or (Eq (a_2 f) (a_3 f)) (Ne (a_2 g) (a_3 g))))) % 4.79/4.97 Clause #100 (by clausification #[99]): ∀ (a : b) (a_1 : (b → Prop) → Sort _abstMVar.0) (a_2 a_3 : (x : b → Prop) → a_1 x), % 4.79/4.97 Or (Eq (f (skS.0 0 a)) True) (Or (Eq (g (skS.0 0 a)) True) (Or (Eq (a_2 f) (a_3 f)) (Ne (a_2 g) (a_3 g)))) % 4.79/4.97 Clause #101 (by equality resolution #[100]): ∀ (a : b), Or (Eq (f (skS.0 0 a)) True) (Or (Eq (g (skS.0 0 a)) True) (Eq ((fun x => x) f) ((fun x x => g x) f))) % 4.79/4.97 Clause #109 (by betaEtaReduce #[101]): ∀ (a : b), Or (Eq (f (skS.0 0 a)) True) (Or (Eq (g (skS.0 0 a)) True) (Eq f g)) % 4.79/4.97 Clause #110 (by superposition #[109, 22]): ∀ (a : b), Or (Eq (f (skS.0 0 a)) True) (Or (Eq f g) (Or (Eq (f (skS.0 0 a)) True) (Eq True False))) % 4.82/4.99 Clause #120 (by clausification #[110]): ∀ (a : b), Or (Eq (f (skS.0 0 a)) True) (Or (Eq f g) (Eq (f (skS.0 0 a)) True)) % 4.82/4.99 Clause #121 (by eliminate duplicate literals #[120]): ∀ (a : b), Or (Eq (f (skS.0 0 a)) True) (Eq f g) % 4.82/4.99 Clause #122 (by superposition #[121, 52]): ∀ (a : (b → Prop) → Prop) (a_1 : b), % 4.82/4.99 Or (Eq f g) (Or (Eq (a g) True) (Or (Eq True False) (Or (Eq (g (skS.0 0 a_1)) False) (Eq (a f) False)))) % 4.82/4.99 Clause #129 (by superposition #[121, 23]): ∀ (a : b), Or (Eq f g) (Or (Eq True False) (Eq (g (skS.0 0 a)) True)) % 4.82/4.99 Clause #133 (by clausification #[129]): ∀ (a : b), Or (Eq f g) (Eq (g (skS.0 0 a)) True) % 4.82/4.99 Clause #141 (by clausification #[122]): ∀ (a : (b → Prop) → Prop) (a_1 : b), Or (Eq f g) (Or (Eq (a g) True) (Or (Eq (g (skS.0 0 a_1)) False) (Eq (a f) False))) % 4.82/4.99 Clause #142 (by superposition #[141, 133]): ∀ (a : (b → Prop) → Prop), Or (Eq f g) (Or (Eq (a g) True) (Or (Eq (a f) False) (Or (Eq f g) (Eq False True)))) % 4.82/4.99 Clause #157 (by clausification #[142]): ∀ (a : (b → Prop) → Prop), Or (Eq f g) (Or (Eq (a g) True) (Or (Eq (a f) False) (Eq f g))) % 4.82/4.99 Clause #159 (by neHoist #[157]): ∀ (a : (b → Prop) → Sort _abstMVar.1) (a_1 a_2 : (x : b → Prop) → a x), % 4.82/4.99 Or (Eq f g) (Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) g) True) (Or (Eq f g) (Or (Eq True False) (Eq (a_1 f) (a_2 f))))) % 4.82/4.99 Clause #202 (by betaEtaReduce #[159]): ∀ (a : (b → Prop) → Sort _abstMVar.1) (a_1 a_2 : (x : b → Prop) → a x), % 4.82/4.99 Or (Eq f g) (Or (Eq (Ne (a_1 g) (a_2 g)) True) (Or (Eq f g) (Or (Eq True False) (Eq (a_1 f) (a_2 f))))) % 4.82/4.99 Clause #203 (by clausification #[202]): ∀ (a : (b → Prop) → Sort _abstMVar.2) (a_1 a_2 : (x : b → Prop) → a x), % 4.82/4.99 Or (Eq f g) (Or (Eq f g) (Or (Eq True False) (Or (Eq (a_1 f) (a_2 f)) (Ne (a_1 g) (a_2 g))))) % 4.82/4.99 Clause #204 (by clausification #[203]): ∀ (a : (b → Prop) → Sort _abstMVar.2) (a_1 a_2 : (x : b → Prop) → a x), % 4.82/4.99 Or (Eq f g) (Or (Eq f g) (Or (Eq (a_1 f) (a_2 f)) (Ne (a_1 g) (a_2 g)))) % 4.82/4.99 Clause #205 (by equality resolution #[204]): Or (Eq f g) (Or (Eq f g) (Eq ((fun x => x) f) ((fun x x => g x) f))) % 4.82/4.99 Clause #212 (by betaEtaReduce #[205]): Or (Eq f g) (Or (Eq f g) (Eq f g)) % 4.82/4.99 Clause #213 (by equality factoring #[212]): Or (Eq f g) (Or (Ne f f) (Eq f g)) % 4.82/4.99 Clause #214 (by eliminate resolved literals #[213]): Or (Eq f g) (Eq f g) % 4.82/4.99 Clause #215 (by equality factoring #[214]): Or (Ne f f) (Eq f g) % 4.82/4.99 Clause #218 (by eliminate resolved literals #[215]): Eq f g % 4.82/4.99 Clause #236 (by backward positive simplify reflect #[218, 29]): False % 4.82/4.99 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------