%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV220^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:02:57 PM UTC 2025 % Result : Theorem 3.70s 3.90s % Output : Proof 3.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.12 % Problem : SEV220^5 : TPTP v9.2.0. Released v4.0.0. % 0.05/0.13 % Command : duper %s % 0.13/0.34 % Computer : n004.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 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 01:21:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.70/3.90 SZS status Theorem for theBenchmark.p % 3.70/3.90 SZS output start Proof for theBenchmark.p % 3.70/3.90 Clause #0 (by assumption #[]): Eq % 3.70/3.90 (Not % 3.70/3.90 (∀ (Xx : a), % 3.70/3.90 (Exists fun Xt => And (∀ (S : b → Prop), w S → S Xt) (Eq Xx (f Xt))) → % 3.70/3.90 ∀ (S : a → Prop), % 3.70/3.90 (Exists fun Xt => And (w Xt) (Eq S fun Xz => Exists fun Xt0 => And (Xt Xt0) (Eq Xz (f Xt0)))) → S Xx)) % 3.70/3.90 True % 3.70/3.90 Clause #1 (by clausification #[0]): Eq % 3.70/3.90 (∀ (Xx : a), % 3.70/3.90 (Exists fun Xt => And (∀ (S : b → Prop), w S → S Xt) (Eq Xx (f Xt))) → % 3.70/3.90 ∀ (S : a → Prop), % 3.70/3.90 (Exists fun Xt => And (w Xt) (Eq S fun Xz => Exists fun Xt0 => And (Xt Xt0) (Eq Xz (f Xt0)))) → S Xx) % 3.70/3.90 False % 3.70/3.90 Clause #2 (by clausification #[1]): ∀ (a_1 : a), % 3.70/3.90 Eq % 3.70/3.90 (Not % 3.70/3.90 ((Exists fun Xt => And (∀ (S : b → Prop), w S → S Xt) (Eq (skS.0 0 a_1) (f Xt))) → % 3.70/3.90 ∀ (S : a → Prop), % 3.70/3.90 (Exists fun Xt => And (w Xt) (Eq S fun Xz => Exists fun Xt0 => And (Xt Xt0) (Eq Xz (f Xt0)))) → % 3.70/3.90 S (skS.0 0 a_1))) % 3.70/3.90 True % 3.70/3.90 Clause #3 (by clausification #[2]): ∀ (a_1 : a), % 3.70/3.90 Eq % 3.70/3.90 ((Exists fun Xt => And (∀ (S : b → Prop), w S → S Xt) (Eq (skS.0 0 a_1) (f Xt))) → % 3.70/3.90 ∀ (S : a → Prop), % 3.70/3.90 (Exists fun Xt => And (w Xt) (Eq S fun Xz => Exists fun Xt0 => And (Xt Xt0) (Eq Xz (f Xt0)))) → S (skS.0 0 a_1)) % 3.70/3.90 False % 3.70/3.90 Clause #4 (by clausification #[3]): ∀ (a_1 : a), Eq (Exists fun Xt => And (∀ (S : b → Prop), w S → S Xt) (Eq (skS.0 0 a_1) (f Xt))) True % 3.70/3.90 Clause #5 (by clausification #[3]): ∀ (a_1 : a), % 3.70/3.90 Eq % 3.70/3.90 (∀ (S : a → Prop), % 3.70/3.90 (Exists fun Xt => And (w Xt) (Eq S fun Xz => Exists fun Xt0 => And (Xt Xt0) (Eq Xz (f Xt0)))) → S (skS.0 0 a_1)) % 3.70/3.90 False % 3.70/3.90 Clause #6 (by clausification #[4]): ∀ (a_1 : a) (a_2 : b), % 3.70/3.90 Eq (And (∀ (S : b → Prop), w S → S (skS.0 1 a_1 a_2)) (Eq (skS.0 0 a_1) (f (skS.0 1 a_1 a_2)))) True % 3.70/3.90 Clause #7 (by clausification #[6]): ∀ (a_1 : a) (a_2 : b), Eq (Eq (skS.0 0 a_1) (f (skS.0 1 a_1 a_2))) True % 3.70/3.90 Clause #8 (by clausification #[6]): ∀ (a_1 : a) (a_2 : b), Eq (∀ (S : b → Prop), w S → S (skS.0 1 a_1 a_2)) True % 3.70/3.90 Clause #9 (by clausification #[7]): ∀ (a_1 : a) (a_2 : b), Eq (skS.0 0 a_1) (f (skS.0 1 a_1 a_2)) % 3.70/3.90 Clause #10 (by clausification #[5]): ∀ (a_1 : a) (a_2 : a → Prop), % 3.70/3.90 Eq % 3.70/3.90 (Not % 3.70/3.90 ((Exists fun Xt => And (w Xt) (Eq (skS.0 2 a_1 a_2) fun Xz => Exists fun Xt0 => And (Xt Xt0) (Eq Xz (f Xt0)))) → % 3.70/3.90 skS.0 2 a_1 a_2 (skS.0 0 a_1))) % 3.70/3.90 True % 3.70/3.90 Clause #11 (by clausification #[10]): ∀ (a_1 : a) (a_2 : a → Prop), % 3.70/3.90 Eq % 3.70/3.90 ((Exists fun Xt => And (w Xt) (Eq (skS.0 2 a_1 a_2) fun Xz => Exists fun Xt0 => And (Xt Xt0) (Eq Xz (f Xt0)))) → % 3.70/3.90 skS.0 2 a_1 a_2 (skS.0 0 a_1)) % 3.70/3.90 False % 3.70/3.90 Clause #12 (by clausification #[11]): ∀ (a_1 : a) (a_2 : a → Prop), % 3.70/3.90 Eq (Exists fun Xt => And (w Xt) (Eq (skS.0 2 a_1 a_2) fun Xz => Exists fun Xt0 => And (Xt Xt0) (Eq Xz (f Xt0)))) True % 3.70/3.90 Clause #13 (by clausification #[11]): ∀ (a_1 : a) (a_2 : a → Prop), Eq (skS.0 2 a_1 a_2 (skS.0 0 a_1)) False % 3.70/3.90 Clause #14 (by clausification #[12]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : b → Prop), % 3.70/3.90 Eq % 3.70/3.90 (And (w (skS.0 3 a_1 a_2 a_3)) % 3.70/3.90 (Eq (skS.0 2 a_1 a_2) fun Xz => Exists fun Xt0 => And (skS.0 3 a_1 a_2 a_3 Xt0) (Eq Xz (f Xt0)))) % 3.70/3.90 True % 3.70/3.90 Clause #15 (by clausification #[14]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : b → Prop), % 3.70/3.90 Eq (Eq (skS.0 2 a_1 a_2) fun Xz => Exists fun Xt0 => And (skS.0 3 a_1 a_2 a_3 Xt0) (Eq Xz (f Xt0))) True % 3.70/3.90 Clause #16 (by clausification #[14]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : b → Prop), Eq (w (skS.0 3 a_1 a_2 a_3)) True % 3.70/3.90 Clause #17 (by clausification #[15]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : b → Prop), % 3.70/3.90 Eq (skS.0 2 a_1 a_2) fun Xz => Exists fun Xt0 => And (skS.0 3 a_1 a_2 a_3 Xt0) (Eq Xz (f Xt0)) % 3.70/3.90 Clause #18 (by argument congruence #[17]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a) (a_4 : b → Prop), % 3.70/3.90 Eq (skS.0 2 a_1 a_2 a_3) ((fun Xz => Exists fun Xt0 => And (skS.0 3 a_1 a_2 a_4 Xt0) (Eq Xz (f Xt0))) a_3) % 3.70/3.90 Clause #19 (by clausification #[8]): ∀ (a_1 : b → Prop) (a_2 : a) (a_3 : b), Eq (w a_1 → a_1 (skS.0 1 a_2 a_3)) True % 3.70/3.90 Clause #20 (by clausification #[19]): ∀ (a_1 : b → Prop) (a_2 : a) (a_3 : b), Or (Eq (w a_1) False) (Eq (a_1 (skS.0 1 a_2 a_3)) True) % 3.70/3.92 Clause #21 (by superposition #[16, 20]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : b → Prop) (a_4 : a) (a_5 : b), % 3.70/3.92 Or (Eq ((fun x => skS.0 3 a_1 a_2 a_3 x) (skS.0 1 a_4 a_5)) True) (Eq False True) % 3.70/3.92 Clause #23 (by betaEtaReduce #[18]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a) (a_4 : b → Prop), % 3.70/3.92 Eq (skS.0 2 a_1 a_2 a_3) (Exists fun Xt0 => And (skS.0 3 a_1 a_2 a_4 Xt0) (Eq a_3 (f Xt0))) % 3.70/3.92 Clause #26 (by existsHoist #[23]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a) (a_4 : b → Prop) (a_5 : b), % 3.70/3.92 Or (Eq (skS.0 2 a_1 a_2 a_3) True) (Eq ((fun Xt0 => And (skS.0 3 a_1 a_2 a_4 Xt0) (Eq a_3 (f Xt0))) a_5) False) % 3.70/3.92 Clause #29 (by betaEtaReduce #[21]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : b → Prop) (a_4 : a) (a_5 : b), % 3.70/3.92 Or (Eq (skS.0 3 a_1 a_2 a_3 (skS.0 1 a_4 a_5)) True) (Eq False True) % 3.70/3.92 Clause #30 (by clausification #[29]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : b → Prop) (a_4 : a) (a_5 : b), Eq (skS.0 3 a_1 a_2 a_3 (skS.0 1 a_4 a_5)) True % 3.70/3.92 Clause #32 (by betaEtaReduce #[26]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a) (a_4 : b → Prop) (a_5 : b), % 3.70/3.92 Or (Eq (skS.0 2 a_1 a_2 a_3) True) (Eq (And (skS.0 3 a_1 a_2 a_4 a_5) (Eq a_3 (f a_5))) False) % 3.70/3.92 Clause #33 (by clausification #[32]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a) (a_4 : b → Prop) (a_5 : b), % 3.70/3.92 Or (Eq (skS.0 2 a_1 a_2 a_3) True) (Or (Eq (skS.0 3 a_1 a_2 a_4 a_5) False) (Eq (Eq a_3 (f a_5)) False)) % 3.70/3.92 Clause #34 (by clausification #[33]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a) (a_4 : b → Prop) (a_5 : b), % 3.70/3.92 Or (Eq (skS.0 2 a_1 a_2 a_3) True) (Or (Eq (skS.0 3 a_1 a_2 a_4 a_5) False) (Ne a_3 (f a_5))) % 3.70/3.92 Clause #35 (by destructive equality resolution #[34]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : b) (a_4 : b → Prop), % 3.70/3.92 Or (Eq (skS.0 2 a_1 a_2 (f a_3)) True) (Eq (skS.0 3 a_1 a_2 a_4 a_3) False) % 3.70/3.92 Clause #36 (by superposition #[35, 30]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a) (a_4 : b), % 3.70/3.92 Or (Eq (skS.0 2 a_1 (fun x => a_2 x) (f (skS.0 1 a_3 a_4))) True) (Eq False True) % 3.70/3.92 Clause #38 (by betaEtaReduce #[36]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a) (a_4 : b), Or (Eq (skS.0 2 a_1 a_2 (f (skS.0 1 a_3 a_4))) True) (Eq False True) % 3.70/3.92 Clause #39 (by clausification #[38]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a) (a_4 : b), Eq (skS.0 2 a_1 a_2 (f (skS.0 1 a_3 a_4))) True % 3.70/3.92 Clause #40 (by forward demodulation #[39, 9]): ∀ (a_1 : a) (a_2 : a → Prop) (a_3 : a), Eq (skS.0 2 a_1 a_2 (skS.0 0 a_3)) True % 3.70/3.92 Clause #41 (by superposition #[40, 13]): Eq True False % 3.70/3.92 Clause #42 (by clausification #[41]): False % 3.70/3.92 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------