%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN375+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:07:32 PM UTC 2025 % Result : Theorem 4.43s 4.63s % Output : Proof 4.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN375+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.13 % Command : duper %s % 0.14/0.35 % Computer : n026.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Oct 2 15:34:53 EDT 2025 % 0.14/0.35 % CPUTime : % 4.43/4.63 SZS status Theorem for theBenchmark.p % 4.43/4.63 SZS output start Proof for theBenchmark.p % 4.43/4.63 Clause #0 (by assumption #[]): Eq % 4.43/4.63 (Not % 4.43/4.63 (Iff (∀ (X : Iota), Iff (big_p X) (Exists fun Y => big_p Y)) % 4.43/4.63 (Iff (∀ (X : Iota), big_p X) (Exists fun Y => big_p Y)))) % 4.43/4.63 True % 4.43/4.63 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (∀ (X : Iota), Iff (big_p X) (Exists big_p)) (Iff (∀ (X : Iota), big_p X) (Exists big_p)))) True % 4.43/4.63 Clause #2 (by clausification #[1]): Eq (Iff (∀ (X : Iota), Iff (big_p X) (Exists big_p)) (Iff (∀ (X : Iota), big_p X) (Exists big_p))) False % 4.43/4.63 Clause #3 (by clausification #[2]): Or (Eq (∀ (X : Iota), Iff (big_p X) (Exists big_p)) False) (Eq (Iff (∀ (X : Iota), big_p X) (Exists big_p)) False) % 4.43/4.63 Clause #4 (by clausification #[2]): Or (Eq (∀ (X : Iota), Iff (big_p X) (Exists big_p)) True) (Eq (Iff (∀ (X : Iota), big_p X) (Exists big_p)) True) % 4.43/4.63 Clause #5 (by clausification #[3]): ∀ (a : Iota), % 4.43/4.63 Or (Eq (Iff (∀ (X : Iota), big_p X) (Exists big_p)) False) (Eq (Not (Iff (big_p (skS.0 0 a)) (Exists big_p))) True) % 4.43/4.63 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 4.43/4.63 Or (Eq (Not (Iff (big_p (skS.0 0 a)) (Exists big_p))) True) % 4.43/4.63 (Or (Eq (∀ (X : Iota), big_p X) False) (Eq (Exists big_p) False)) % 4.43/4.63 Clause #7 (by clausification #[5]): ∀ (a : Iota), % 4.43/4.63 Or (Eq (Not (Iff (big_p (skS.0 0 a)) (Exists big_p))) True) % 4.43/4.63 (Or (Eq (∀ (X : Iota), big_p X) True) (Eq (Exists big_p) True)) % 4.43/4.63 Clause #8 (by clausification #[6]): ∀ (a : Iota), % 4.43/4.63 Or (Eq (∀ (X : Iota), big_p X) False) % 4.43/4.63 (Or (Eq (Exists big_p) False) (Eq (Iff (big_p (skS.0 0 a)) (Exists big_p)) False)) % 4.43/4.63 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 4.43/4.63 Or (Eq (Exists big_p) False) % 4.43/4.63 (Or (Eq (Iff (big_p (skS.0 0 a)) (Exists big_p)) False) (Eq (Not (big_p (skS.0 1 a_1))) True)) % 4.43/4.63 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.43/4.63 Or (Eq (Iff (big_p (skS.0 0 a)) (Exists big_p)) False) % 4.43/4.63 (Or (Eq (Not (big_p (skS.0 1 a_1))) True) (Eq (big_p a_2) False)) % 4.43/4.63 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.43/4.63 Or (Eq (Not (big_p (skS.0 1 a))) True) % 4.43/4.63 (Or (Eq (big_p a_1) False) (Or (Eq (big_p (skS.0 0 a_2)) False) (Eq (Exists big_p) False))) % 4.43/4.63 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.43/4.63 Or (Eq (big_p a) False) % 4.43/4.63 (Or (Eq (big_p (skS.0 0 a_1)) False) (Or (Eq (Exists big_p) False) (Eq (big_p (skS.0 1 a_2)) False))) % 4.43/4.63 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 4.43/4.63 Or (Eq (big_p a) False) % 4.43/4.63 (Or (Eq (big_p (skS.0 0 a_1)) False) (Or (Eq (big_p (skS.0 1 a_2)) False) (Eq (big_p a_3) False))) % 4.43/4.63 Clause #15 (by clausification #[4]): ∀ (a : Iota), Or (Eq (Iff (∀ (X : Iota), big_p X) (Exists big_p)) True) (Eq (Iff (big_p a) (Exists big_p)) True) % 4.43/4.63 Clause #16 (by clausification #[15]): ∀ (a : Iota), % 4.43/4.63 Or (Eq (Iff (big_p a) (Exists big_p)) True) (Or (Eq (∀ (X : Iota), big_p X) True) (Eq (Exists big_p) False)) % 4.43/4.63 Clause #18 (by clausification #[16]): ∀ (a : Iota), % 4.43/4.63 Or (Eq (∀ (X : Iota), big_p X) True) (Or (Eq (Exists big_p) False) (Or (Eq (big_p a) True) (Eq (Exists big_p) False))) % 4.43/4.63 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), % 4.43/4.63 Or (Eq (Exists big_p) False) (Or (Eq (big_p a) True) (Or (Eq (Exists big_p) False) (Eq (big_p a_1) True))) % 4.43/4.63 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), % 4.43/4.63 Or (Eq (big_p a) True) (Or (Eq (Exists big_p) False) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) False))) % 4.43/4.63 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), % 4.43/4.63 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) False) (Eq (big_p a_3) False))) % 4.43/4.63 Clause #36 (by clausification #[7]): ∀ (a : Iota), % 4.43/4.63 Or (Eq (∀ (X : Iota), big_p X) True) (Or (Eq (Exists big_p) True) (Eq (Iff (big_p (skS.0 0 a)) (Exists big_p)) False)) % 4.43/4.63 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 4.43/4.63 Or (Eq (Exists big_p) True) (Or (Eq (Iff (big_p (skS.0 0 a)) (Exists big_p)) False) (Eq (big_p a_1) True)) % 4.43/4.63 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 4.43/4.63 Or (Eq (Iff (big_p (skS.0 0 a)) (Exists big_p)) False) (Or (Eq (big_p a_1) True) (Eq (big_p (skS.0 8 a_2)) True)) % 4.43/4.63 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 4.43/4.66 Or (Eq (big_p a) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 8 a_1)) True) (Or (Eq (big_p (skS.0 0 a_2)) True) (Eq (Exists big_p) True))) % 4.43/4.66 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 4.43/4.66 Or (Eq (big_p a) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 8 a_1)) True) (Or (Eq (big_p (skS.0 0 a_2)) True) (Eq (big_p (skS.0 9 a_3)) True))) % 4.43/4.66 Clause #53 (by equality factoring #[42]): ∀ (a a_1 a_2 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 0 a_1)) True) (Or (Ne True True) (Eq (big_p (skS.0 9 a_2)) True))) % 4.43/4.66 Clause #56 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 0 a_1)) True) (Or (Eq (big_p (skS.0 9 a_2)) True) (Or (Eq True False) (Eq True False)))) % 4.43/4.66 Clause #58 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 0 a_1)) True) (Or (Eq (big_p (skS.0 9 a_2)) True) (Eq True False))) % 4.43/4.66 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) (Or (Eq (big_p (skS.0 0 a_1)) True) (Eq (big_p (skS.0 9 a_2)) True)) % 4.43/4.66 Clause #63 (by superposition #[59, 22]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 9 a_1)) True) % 4.43/4.66 (Or (Eq (big_p a_2) True) (Or (Eq (big_p a_3) True) (Or (Eq True False) (Eq (big_p a_4) False))))) % 4.43/4.66 Clause #75 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 9 a_1)) True) (Or (Eq (big_p a_2) True) (Or (Eq (big_p a_3) True) (Eq (big_p a_4) False)))) % 4.43/4.66 Clause #77 (by superposition #[75, 59]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 9 a_1)) True) % 4.43/4.66 (Or (Eq (big_p a_2) True) % 4.43/4.66 (Or (Eq (big_p a_3) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 8 a_4)) True) (Or (Eq False True) (Eq (big_p (skS.0 9 a_5)) True)))))) % 4.43/4.66 Clause #98 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 9 a_1)) True) % 4.43/4.66 (Or (Eq (big_p a_2) True) % 4.43/4.66 (Or (Eq (big_p a_3) True) (Or (Eq (big_p (skS.0 8 a_4)) True) (Eq (big_p (skS.0 9 a_5)) True))))) % 4.43/4.66 Clause #127 (by equality factoring #[98]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p a_1) True) % 4.43/4.66 (Or (Eq (big_p a_2) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 8 a_3)) True) (Or (Ne True True) (Eq (big_p (skS.0 9 a_4)) True))))) % 4.43/4.66 Clause #131 (by clausification #[127]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p a_1) True) % 4.43/4.66 (Or (Eq (big_p a_2) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 8 a_3)) True) (Or (Eq (big_p (skS.0 9 a_4)) True) (Or (Eq True False) (Eq True False)))))) % 4.43/4.66 Clause #133 (by clausification #[131]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p a_1) True) % 4.43/4.66 (Or (Eq (big_p a_2) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 8 a_3)) True) (Or (Eq (big_p (skS.0 9 a_4)) True) (Eq True False))))) % 4.43/4.66 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.43/4.66 Or (Eq (big_p (skS.0 8 a)) True) % 4.43/4.66 (Or (Eq (big_p a_1) True) % 4.43/4.66 (Or (Eq (big_p a_2) True) (Or (Eq (big_p (skS.0 8 a_3)) True) (Eq (big_p (skS.0 9 a_4)) True)))) % 4.43/4.66 Clause #156 (by equality factoring #[134]): ∀ (a a_1 a_2 a_3 : Iota), % 4.43/4.66 Or (Eq (big_p a) True) % 4.43/4.66 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 9 a_2)) True) (Or (Ne True True) (Eq (big_p (skS.0 8 a_3)) True)))) % 4.43/4.66 Clause #160 (by clausification #[156]): ∀ (a a_1 a_2 a_3 : Iota), % 4.43/4.66 Or (Eq (big_p a) True) % 4.43/4.66 (Or (Eq (big_p a_1) True) % 4.43/4.66 (Or (Eq (big_p (skS.0 9 a_2)) True) (Or (Eq (big_p (skS.0 8 a_3)) True) (Or (Eq True False) (Eq True False))))) % 4.43/4.66 Clause #162 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota), % 4.43/4.66 Or (Eq (big_p a) True) % 4.43/4.66 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 9 a_2)) True) (Or (Eq (big_p (skS.0 8 a_3)) True) (Eq True False)))) % 4.43/4.66 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 : Iota), % 4.43/4.66 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 9 a_2)) True) (Eq (big_p (skS.0 8 a_3)) True))) % 4.53/4.68 Clause #181 (by equality factoring #[163]): ∀ (a a_1 a_2 : Iota), % 4.53/4.68 Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 9 a_1)) True) (Or (Ne True True) (Eq (big_p (skS.0 8 a_2)) True))) % 4.53/4.68 Clause #182 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), % 4.53/4.68 Or (Eq (big_p a) True) % 4.53/4.68 (Or (Eq (big_p (skS.0 9 a_1)) True) (Or (Eq (big_p (skS.0 8 a_2)) True) (Or (Eq True False) (Eq True False)))) % 4.53/4.68 Clause #184 (by clausification #[182]): ∀ (a a_1 a_2 : Iota), % 4.53/4.68 Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 9 a_1)) True) (Or (Eq (big_p (skS.0 8 a_2)) True) (Eq True False))) % 4.53/4.68 Clause #185 (by clausification #[184]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 9 a_1)) True) (Eq (big_p (skS.0 8 a_2)) True)) % 4.53/4.68 Clause #202 (by equality factoring #[185]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Or (Ne True True) (Eq (big_p (skS.0 8 a_1)) True)) % 4.53/4.68 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota), % 4.53/4.68 Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p (skS.0 8 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.53/4.68 Clause #205 (by clausification #[203]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p (skS.0 8 a_1)) True) (Eq True False)) % 4.53/4.68 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Eq (big_p (skS.0 8 a_1)) True) % 4.53/4.68 Clause #212 (by superposition #[206, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 4.53/4.68 Or (Eq (big_p (skS.0 9 a)) True) % 4.53/4.68 (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Or (Eq True False) (Eq (big_p a_3) False)))) % 4.53/4.68 Clause #223 (by clausification #[212]): ∀ (a a_1 a_2 a_3 : Iota), % 4.53/4.68 Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Eq (big_p a_3) False))) % 4.53/4.68 Clause #225 (by superposition #[223, 206]): ∀ (a a_1 a_2 a_3 : Iota), % 4.53/4.68 Or (Eq (big_p (skS.0 9 a)) True) % 4.53/4.68 (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Or (Eq (big_p (skS.0 9 a_3)) True) (Eq False True)))) % 4.53/4.68 Clause #267 (by clausification #[225]): ∀ (a a_1 a_2 a_3 : Iota), % 4.53/4.68 Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Eq (big_p (skS.0 9 a_3)) True))) % 4.53/4.68 Clause #279 (by equality factoring #[267]): ∀ (a a_1 a_2 : Iota), % 4.53/4.68 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Ne True True) (Eq (big_p (skS.0 9 a_2)) True))) % 4.53/4.68 Clause #282 (by clausification #[279]): ∀ (a a_1 a_2 : Iota), % 4.53/4.68 Or (Eq (big_p a) True) % 4.53/4.68 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 9 a_2)) True) (Or (Eq True False) (Eq True False)))) % 4.53/4.68 Clause #284 (by clausification #[282]): ∀ (a a_1 a_2 : Iota), % 4.53/4.68 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 9 a_2)) True) (Eq True False))) % 4.53/4.68 Clause #285 (by clausification #[284]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Eq (big_p (skS.0 9 a_2)) True)) % 4.53/4.68 Clause #293 (by equality factoring #[285]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Ne True True) (Eq (big_p (skS.0 9 a_1)) True)) % 4.53/4.68 Clause #295 (by clausification #[293]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 9 a_1)) True) (Or (Eq True False) (Eq True False))) % 4.53/4.68 Clause #297 (by clausification #[295]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 9 a_1)) True) (Eq True False)) % 4.53/4.68 Clause #298 (by clausification #[297]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p (skS.0 9 a_1)) True) % 4.53/4.68 Clause #305 (by equality factoring #[298]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 9 a)) True) % 4.53/4.68 Clause #306 (by clausification #[305]): ∀ (a : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Or (Eq True False) (Eq True False)) % 4.53/4.68 Clause #308 (by clausification #[306]): ∀ (a : Iota), Or (Eq (big_p (skS.0 9 a)) True) (Eq True False) % 4.53/4.68 Clause #309 (by clausification #[308]): ∀ (a : Iota), Eq (big_p (skS.0 9 a)) True % 4.53/4.68 Clause #310 (by superposition #[309, 14]): ∀ (a a_1 a_2 : Iota), % 4.53/4.68 Or (Eq True False) (Or (Eq (big_p (skS.0 0 a)) False) (Or (Eq (big_p (skS.0 1 a_1)) False) (Eq (big_p a_2) False))) % 4.53/4.68 Clause #311 (by superposition #[309, 22]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Eq True False) (Eq (big_p a_2) False))) % 4.54/4.69 Clause #313 (by clausification #[311]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Eq (big_p a_2) False)) % 4.54/4.69 Clause #314 (by superposition #[313, 309]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Eq False True)) % 4.54/4.69 Clause #315 (by clausification #[314]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p a_1) True) % 4.54/4.69 Clause #316 (by equality factoring #[315]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p a) True) % 4.54/4.69 Clause #317 (by clausification #[316]): ∀ (a : Iota), Or (Eq (big_p a) True) (Or (Eq True False) (Eq True False)) % 4.54/4.69 Clause #319 (by clausification #[317]): ∀ (a : Iota), Or (Eq (big_p a) True) (Eq True False) % 4.54/4.69 Clause #320 (by clausification #[319]): ∀ (a : Iota), Eq (big_p a) True % 4.54/4.69 Clause #333 (by clausification #[310]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 0 a)) False) (Or (Eq (big_p (skS.0 1 a_1)) False) (Eq (big_p a_2) False)) % 4.54/4.69 Clause #334 (by superposition #[333, 320]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Or (Eq (big_p a_1) False) (Eq False True)) % 4.54/4.69 Clause #335 (by clausification #[334]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Eq (big_p a_1) False) % 4.54/4.69 Clause #336 (by superposition #[335, 320]): ∀ (a : Iota), Or (Eq (big_p a) False) (Eq False True) % 4.54/4.69 Clause #337 (by clausification #[336]): ∀ (a : Iota), Eq (big_p a) False % 4.54/4.69 Clause #338 (by superposition #[337, 320]): Eq False True % 4.54/4.69 Clause #339 (by clausification #[338]): False % 4.54/4.69 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------