%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO266^5 : 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 08:08:49 PM UTC 2025 % Result : Theorem 4.28s 4.44s % Output : Proof 4.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO266^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.14/0.35 % Computer : n004.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 : Fri Oct 3 14:36:53 EDT 2025 % 0.14/0.35 % CPUTime : % 4.28/4.44 SZS status Theorem for theBenchmark.p % 4.28/4.44 SZS output start Proof for theBenchmark.p % 4.28/4.44 Clause #0 (by assumption #[]): Eq % 4.28/4.44 (Not % 4.28/4.44 (Iff (Exists fun S => ∀ (X : Iota), And (Or (S X) (cP X)) (Or (Not (S X)) (cQ X))) % 4.28/4.44 (∀ (Y : Iota), Or (cP Y) (cQ Y)))) % 4.28/4.44 True % 4.28/4.44 Clause #1 (by clausification #[0]): Eq (Iff (Exists fun S => ∀ (X : Iota), And (Or (S X) (cP X)) (Or (Not (S X)) (cQ X))) (∀ (Y : Iota), Or (cP Y) (cQ Y))) % 4.28/4.44 False % 4.28/4.44 Clause #2 (by clausification #[1]): Or (Eq (Exists fun S => ∀ (X : Iota), And (Or (S X) (cP X)) (Or (Not (S X)) (cQ X))) False) % 4.28/4.44 (Eq (∀ (Y : Iota), Or (cP Y) (cQ Y)) False) % 4.28/4.44 Clause #3 (by clausification #[1]): Or (Eq (Exists fun S => ∀ (X : Iota), And (Or (S X) (cP X)) (Or (Not (S X)) (cQ X))) True) % 4.28/4.44 (Eq (∀ (Y : Iota), Or (cP Y) (cQ Y)) True) % 4.28/4.44 Clause #4 (by clausification #[2]): ∀ (a : Iota → Prop), % 4.28/4.44 Or (Eq (∀ (Y : Iota), Or (cP Y) (cQ Y)) False) % 4.28/4.44 (Eq (∀ (X : Iota), And (Or (a X) (cP X)) (Or (Not (a X)) (cQ X))) False) % 4.28/4.44 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.28/4.44 Or (Eq (∀ (X : Iota), And (Or (a X) (cP X)) (Or (Not (a X)) (cQ X))) False) % 4.28/4.44 (Eq (Not (Or (cP (skS.0 0 a_1)) (cQ (skS.0 0 a_1)))) True) % 4.28/4.44 Clause #6 (by clausification #[5]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.44 Or (Eq (Not (Or (cP (skS.0 0 a)) (cQ (skS.0 0 a)))) True) % 4.28/4.44 (Eq % 4.28/4.44 (Not % 4.28/4.44 (And (Or (a_1 (skS.0 1 a_1 a_2)) (cP (skS.0 1 a_1 a_2))) % 4.28/4.44 (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))))) % 4.28/4.44 True) % 4.28/4.44 Clause #7 (by clausification #[6]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.44 Or % 4.28/4.44 (Eq (Not (And (Or (a (skS.0 1 a a_1)) (cP (skS.0 1 a a_1))) (Or (Not (a (skS.0 1 a a_1))) (cQ (skS.0 1 a a_1))))) % 4.28/4.44 True) % 4.28/4.44 (Eq (Or (cP (skS.0 0 a_2)) (cQ (skS.0 0 a_2))) False) % 4.28/4.44 Clause #8 (by clausification #[7]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.44 Or (Eq (Or (cP (skS.0 0 a)) (cQ (skS.0 0 a))) False) % 4.28/4.44 (Eq % 4.28/4.44 (And (Or (a_1 (skS.0 1 a_1 a_2)) (cP (skS.0 1 a_1 a_2))) % 4.28/4.44 (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2)))) % 4.28/4.44 False) % 4.28/4.44 Clause #9 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.44 Or (Eq (And (Or (a (skS.0 1 a a_1)) (cP (skS.0 1 a a_1))) (Or (Not (a (skS.0 1 a a_1))) (cQ (skS.0 1 a a_1)))) False) % 4.28/4.44 (Eq (cQ (skS.0 0 a_2)) False) % 4.28/4.44 Clause #10 (by clausification #[8]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.44 Or (Eq (And (Or (a (skS.0 1 a a_1)) (cP (skS.0 1 a a_1))) (Or (Not (a (skS.0 1 a a_1))) (cQ (skS.0 1 a a_1)))) False) % 4.28/4.44 (Eq (cP (skS.0 0 a_2)) False) % 4.28/4.44 Clause #11 (by clausification #[9]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.44 Or (Eq (cQ (skS.0 0 a)) False) % 4.28/4.44 (Or (Eq (Or (a_1 (skS.0 1 a_1 a_2)) (cP (skS.0 1 a_1 a_2))) False) % 4.28/4.44 (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False)) % 4.28/4.44 Clause #12 (by clausification #[11]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.44 Or (Eq (cQ (skS.0 0 a)) False) % 4.28/4.44 (Or (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False) (Eq (cP (skS.0 1 a_1 a_2)) False)) % 4.28/4.44 Clause #13 (by clausification #[11]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.44 Or (Eq (cQ (skS.0 0 a)) False) % 4.28/4.44 (Or (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False) (Eq (a_1 (skS.0 1 a_1 a_2)) False)) % 4.28/4.44 Clause #15 (by clausification #[12]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.44 Or (Eq (cQ (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1 a_2)) False) (Eq (Not (a_1 (skS.0 1 a_1 a_2))) False)) % 4.28/4.44 Clause #16 (by clausification #[3]): ∀ (a : Iota → Prop), % 4.28/4.44 Or (Eq (∀ (Y : Iota), Or (cP Y) (cQ Y)) True) % 4.28/4.44 (Eq (∀ (X : Iota), And (Or (skS.0 2 a X) (cP X)) (Or (Not (skS.0 2 a X)) (cQ X))) True) % 4.28/4.44 Clause #17 (by clausification #[16]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.28/4.44 Or (Eq (∀ (X : Iota), And (Or (skS.0 2 a X) (cP X)) (Or (Not (skS.0 2 a X)) (cQ X))) True) % 4.28/4.44 (Eq (Or (cP a_1) (cQ a_1)) True) % 4.28/4.44 Clause #18 (by clausification #[17]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.44 Or (Eq (Or (cP a) (cQ a)) True) (Eq (And (Or (skS.0 2 a_1 a_2) (cP a_2)) (Or (Not (skS.0 2 a_1 a_2)) (cQ a_2))) True) % 4.28/4.44 Clause #19 (by clausification #[18]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (And (Or (skS.0 2 a a_1) (cP a_1)) (Or (Not (skS.0 2 a a_1)) (cQ a_1))) True) % 4.28/4.47 (Or (Eq (cP a_2) True) (Eq (cQ a_2) True)) % 4.28/4.47 Clause #20 (by clausification #[19]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.47 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Eq (Or (Not (skS.0 2 a_1 a_2)) (cQ a_2)) True)) % 4.28/4.47 Clause #21 (by clausification #[19]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.47 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Eq (Or (skS.0 2 a_1 a_2) (cP a_2)) True)) % 4.28/4.47 Clause #22 (by clausification #[20]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.47 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (Not (skS.0 2 a_1 a_2)) True) (Eq (cQ a_2) True))) % 4.28/4.47 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.28/4.47 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Eq (skS.0 2 a_2 a_1) False))) % 4.28/4.47 Clause #24 (by clausification #[21]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.47 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (skS.0 2 a_1 a_2) True) (Eq (cP a_2) True))) % 4.28/4.47 Clause #25 (by superposition #[24, 23]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (cP a) True) % 4.28/4.47 (Or (Eq (cQ a) True) % 4.28/4.47 (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq (cQ a_2) True) (Or (Eq (cQ a_1) True) (Eq True False)))))) % 4.28/4.47 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (cP a) True) % 4.28/4.47 (Or (Eq (cQ a) True) (Or (Eq (cP a_1) True) (Or (Eq (cP a_2) True) (Or (Eq (cQ a_2) True) (Eq (cQ a_1) True))))) % 4.28/4.47 Clause #29 (by equality factoring #[26]): ∀ (a a_1 : Iota), % 4.28/4.47 Or (Eq (cP a) True) % 4.28/4.47 (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Or (Eq (cQ a_1) True) (Or (Ne True True) (Eq (cP a_1) True))))) % 4.28/4.47 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), % 4.28/4.47 Or (Eq (cP a) True) % 4.28/4.47 (Or (Eq (cQ a) True) % 4.28/4.47 (Or (Eq (cQ a_1) True) (Or (Eq (cQ a_1) True) (Or (Eq (cP a_1) True) (Or (Eq True False) (Eq True False)))))) % 4.28/4.47 Clause #32 (by clausification #[30]): ∀ (a a_1 : Iota), % 4.28/4.47 Or (Eq (cP a) True) % 4.28/4.47 (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Or (Eq (cQ a_1) True) (Or (Eq (cP a_1) True) (Eq True False))))) % 4.28/4.47 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), % 4.28/4.47 Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Or (Eq (cQ a_1) True) (Eq (cP a_1) True)))) % 4.28/4.47 Clause #34 (by eliminate duplicate literals #[33]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cQ a) True) (Or (Eq (cQ a_1) True) (Eq (cP a_1) True))) % 4.28/4.47 Clause #35 (by equality factoring #[34]): ∀ (a : Iota), Or (Eq (cQ a) True) (Or (Eq (cQ a) True) (Or (Ne True True) (Eq (cP a) True))) % 4.28/4.47 Clause #36 (by clausification #[10]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.47 Or (Eq (cP (skS.0 0 a)) False) % 4.28/4.47 (Or (Eq (Or (a_1 (skS.0 1 a_1 a_2)) (cP (skS.0 1 a_1 a_2))) False) % 4.28/4.47 (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False)) % 4.28/4.47 Clause #37 (by clausification #[36]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.47 Or (Eq (cP (skS.0 0 a)) False) % 4.28/4.47 (Or (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False) (Eq (cP (skS.0 1 a_1 a_2)) False)) % 4.28/4.47 Clause #38 (by clausification #[36]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.47 Or (Eq (cP (skS.0 0 a)) False) % 4.28/4.47 (Or (Eq (Or (Not (a_1 (skS.0 1 a_1 a_2))) (cQ (skS.0 1 a_1 a_2))) False) (Eq (a_1 (skS.0 1 a_1 a_2)) False)) % 4.28/4.47 Clause #40 (by clausification #[37]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.47 Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1 a_2)) False) (Eq (Not (a_1 (skS.0 1 a_1 a_2))) False)) % 4.28/4.47 Clause #44 (by clausification #[35]): ∀ (a : Iota), Or (Eq (cQ a) True) (Or (Eq (cQ a) True) (Or (Eq (cP a) True) (Or (Eq True False) (Eq True False)))) % 4.28/4.47 Clause #46 (by clausification #[44]): ∀ (a : Iota), Or (Eq (cQ a) True) (Or (Eq (cQ a) True) (Or (Eq (cP a) True) (Eq True False))) % 4.28/4.47 Clause #47 (by clausification #[46]): ∀ (a : Iota), Or (Eq (cQ a) True) (Or (Eq (cQ a) True) (Eq (cP a) True)) % 4.28/4.47 Clause #48 (by eliminate duplicate literals #[47]): ∀ (a : Iota), Or (Eq (cQ a) True) (Eq (cP a) True) % 4.28/4.47 Clause #59 (by clausification #[13]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.50 Or (Eq (cQ (skS.0 0 a)) False) (Or (Eq (a_1 (skS.0 1 a_1 a_2)) False) (Eq (cQ (skS.0 1 a_1 a_2)) False)) % 4.28/4.50 Clause #61 (by clausification #[40]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.50 Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1 a_2)) False) (Eq (a_1 (skS.0 1 a_1 a_2)) True)) % 4.28/4.50 Clause #62 (by superposition #[61, 48]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.50 Or (Eq (cP (skS.0 1 a a_1)) False) % 4.28/4.50 (Or (Eq (a (skS.0 1 a a_1)) True) (Or (Eq (cQ (skS.0 0 a_2)) True) (Eq False True))) % 4.28/4.50 Clause #63 (by clausification #[15]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.50 Or (Eq (cQ (skS.0 0 a)) False) (Or (Eq (cP (skS.0 1 a_1 a_2)) False) (Eq (a_1 (skS.0 1 a_1 a_2)) True)) % 4.28/4.50 Clause #65 (by clausification #[38]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 : Iota), % 4.28/4.50 Or (Eq (cP (skS.0 0 a)) False) (Or (Eq (a_1 (skS.0 1 a_1 a_2)) False) (Eq (cQ (skS.0 1 a_1 a_2)) False)) % 4.28/4.50 Clause #67 (by superposition #[65, 48]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.50 Or (Eq (a (skS.0 1 a a_1)) False) % 4.28/4.50 (Or (Eq (cQ (skS.0 1 a a_1)) False) (Or (Eq (cQ (skS.0 0 a_2)) True) (Eq False True))) % 4.28/4.50 Clause #69 (by clausification #[67]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.50 Or (Eq (a (skS.0 1 a a_1)) False) (Or (Eq (cQ (skS.0 1 a a_1)) False) (Eq (cQ (skS.0 0 a_2)) True)) % 4.28/4.50 Clause #78 (by fluidLoobHoist #[69]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.50 Or (Eq (cQ (skS.0 1 a a_1)) False) % 4.28/4.50 (Or (Eq (cQ (skS.0 0 a_2)) True) (Or (Eq True False) (Eq (a (skS.0 1 a a_1)) False))) % 4.28/4.50 Clause #80 (by clausification #[78]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.50 Or (Eq (cQ (skS.0 1 a a_1)) False) (Or (Eq (cQ (skS.0 0 a_2)) True) (Eq (a (skS.0 1 a a_1)) False)) % 4.28/4.50 Clause #87 (by clausification #[62]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.50 Or (Eq (cP (skS.0 1 a a_1)) False) (Or (Eq (a (skS.0 1 a a_1)) True) (Eq (cQ (skS.0 0 a_2)) True)) % 4.28/4.50 Clause #88 (by superposition #[87, 48]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.50 Or (Eq (a (skS.0 1 a a_1)) True) (Or (Eq (cQ (skS.0 0 a_2)) True) (Or (Eq (cQ (skS.0 1 a a_1)) True) (Eq False True))) % 4.28/4.50 Clause #91 (by clausification #[88]): ∀ (a : Iota → Prop) (a_1 a_2 : Iota), % 4.28/4.50 Or (Eq (a (skS.0 1 a a_1)) True) (Or (Eq (cQ (skS.0 0 a_2)) True) (Eq (cQ (skS.0 1 a a_1)) True)) % 4.28/4.50 Clause #99 (by equality factoring #[91]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Ne True True) (Eq (cQ (skS.0 1 (fun x => cQ x) a_1)) True)) % 4.28/4.50 Clause #137 (by betaEtaReduce #[99]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Ne True True) (Eq (cQ (skS.0 1 cQ a_1)) True)) % 4.28/4.50 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota), % 4.28/4.50 Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq (cQ (skS.0 1 cQ a_1)) True) (Or (Eq True False) (Eq True False))) % 4.28/4.50 Clause #140 (by clausification #[138]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq (cQ (skS.0 1 cQ a_1)) True) (Eq True False)) % 4.28/4.50 Clause #141 (by clausification #[140]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cQ (skS.0 1 cQ a_1)) True) % 4.28/4.50 Clause #145 (by superposition #[141, 80]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq True False) (Or (Eq (cQ (skS.0 0 a_1)) True) (Eq True False))) % 4.28/4.50 Clause #164 (by clausification #[145]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq (cQ (skS.0 0 a_1)) True) (Eq True False)) % 4.28/4.50 Clause #165 (by clausification #[164]): ∀ (a a_1 : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq (cQ (skS.0 0 a_1)) True) % 4.28/4.50 Clause #168 (by equality factoring #[165]): ∀ (a : Iota), Or (Ne True True) (Eq (cQ (skS.0 0 a)) True) % 4.28/4.50 Clause #178 (by clausification #[168]): ∀ (a : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 4.28/4.50 Clause #180 (by clausification #[178]): ∀ (a : Iota), Or (Eq (cQ (skS.0 0 a)) True) (Eq True False) % 4.28/4.50 Clause #181 (by clausification #[180]): ∀ (a : Iota), Eq (cQ (skS.0 0 a)) True % 4.28/4.50 Clause #183 (by superposition #[181, 59]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq True False) (Or (Eq (a (skS.0 1 a a_1)) False) (Eq (cQ (skS.0 1 a a_1)) False)) % 4.28/4.50 Clause #184 (by superposition #[181, 63]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq True False) (Or (Eq (cP (skS.0 1 a a_1)) False) (Eq (a (skS.0 1 a a_1)) True)) % 4.28/4.51 Clause #185 (by clausification #[183]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a (skS.0 1 a a_1)) False) (Eq (cQ (skS.0 1 a a_1)) False) % 4.28/4.51 Clause #196 (by fluidLoobHoist #[185]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cQ (skS.0 1 a a_1)) False) (Or (Eq True False) (Eq (a (skS.0 1 a a_1)) False)) % 4.28/4.51 Clause #198 (by clausification #[196]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cQ (skS.0 1 a a_1)) False) (Eq (a (skS.0 1 a a_1)) False) % 4.28/4.51 Clause #208 (by clausification #[184]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (cP (skS.0 1 a a_1)) False) (Eq (a (skS.0 1 a a_1)) True) % 4.28/4.51 Clause #209 (by superposition #[208, 48]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a (skS.0 1 a a_1)) True) (Or (Eq (cQ (skS.0 1 a a_1)) True) (Eq False True)) % 4.28/4.51 Clause #214 (by clausification #[209]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a (skS.0 1 a a_1)) True) (Eq (cQ (skS.0 1 a a_1)) True) % 4.28/4.51 Clause #218 (by equality factoring #[214]): ∀ (a : Iota), Or (Ne True True) (Eq (cQ (skS.0 1 (fun x => cQ x) a)) True) % 4.28/4.51 Clause #252 (by betaEtaReduce #[218]): ∀ (a : Iota), Or (Ne True True) (Eq (cQ (skS.0 1 cQ a)) True) % 4.28/4.51 Clause #253 (by clausification #[252]): ∀ (a : Iota), Or (Eq (cQ (skS.0 1 cQ a)) True) (Or (Eq True False) (Eq True False)) % 4.28/4.51 Clause #255 (by clausification #[253]): ∀ (a : Iota), Or (Eq (cQ (skS.0 1 cQ a)) True) (Eq True False) % 4.28/4.51 Clause #256 (by clausification #[255]): ∀ (a : Iota), Eq (cQ (skS.0 1 cQ a)) True % 4.28/4.51 Clause #257 (by superposition #[256, 198]): Or (Eq True False) (Eq True False) % 4.28/4.51 Clause #267 (by clausification #[257]): Eq True False % 4.28/4.51 Clause #268 (by clausification #[267]): False % 4.28/4.51 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------