%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN374+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:07:31 PM UTC 2025 % Result : Theorem 5.63s 5.87s % Output : Proof 5.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SYN374+1 : TPTP v9.2.0. Released v2.0.0. % 0.13/0.14 % Command : duper %s % 0.14/0.36 % Computer : n008.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 15:13:38 EDT 2025 % 0.14/0.36 % CPUTime : % 5.63/5.87 SZS status Theorem for theBenchmark.p % 5.63/5.87 SZS output start Proof for theBenchmark.p % 5.63/5.87 Clause #0 (by assumption #[]): Eq % 5.63/5.87 (Not % 5.63/5.87 (Iff (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y)) % 5.63/5.87 (Iff (Exists fun X => big_p X) (∀ (Y : Iota), big_p Y)))) % 5.63/5.87 True % 5.63/5.87 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y)) (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)))) True % 5.63/5.87 Clause #2 (by clausification #[1]): Eq (Iff (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y)) (Iff (Exists big_p) (∀ (Y : Iota), big_p Y))) False % 5.63/5.87 Clause #3 (by clausification #[2]): Or (Eq (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y)) False) % 5.63/5.87 (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) False) % 5.63/5.87 Clause #4 (by clausification #[2]): Or (Eq (Exists fun X => ∀ (Y : Iota), Iff (big_p X) (big_p Y)) True) % 5.63/5.87 (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) True) % 5.63/5.87 Clause #5 (by clausification #[3]): ∀ (a : Iota), % 5.63/5.87 Or (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) False) (Eq (∀ (Y : Iota), Iff (big_p a) (big_p Y)) False) % 5.63/5.87 Clause #6 (by clausification #[5]): ∀ (a : Iota), % 5.63/5.87 Or (Eq (∀ (Y : Iota), Iff (big_p a) (big_p Y)) False) % 5.63/5.87 (Or (Eq (Exists big_p) False) (Eq (∀ (Y : Iota), big_p Y) False)) % 5.63/5.87 Clause #7 (by clausification #[5]): ∀ (a : Iota), % 5.63/5.87 Or (Eq (∀ (Y : Iota), Iff (big_p a) (big_p Y)) False) (Or (Eq (Exists big_p) True) (Eq (∀ (Y : Iota), big_p Y) True)) % 5.63/5.87 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota), % 5.63/5.87 Or (Eq (Exists big_p) False) % 5.63/5.87 (Or (Eq (∀ (Y : Iota), big_p Y) False) (Eq (Not (Iff (big_p a) (big_p (skS.0 0 a a_1)))) True)) % 5.63/5.87 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 5.63/5.87 Or (Eq (∀ (Y : Iota), big_p Y) False) % 5.63/5.87 (Or (Eq (Not (Iff (big_p a) (big_p (skS.0 0 a a_1)))) True) (Eq (big_p a_2) False)) % 5.63/5.87 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 5.63/5.87 Or (Eq (Not (Iff (big_p a) (big_p (skS.0 0 a a_1)))) True) % 5.63/5.87 (Or (Eq (big_p a_2) False) (Eq (Not (big_p (skS.0 1 a_3))) True)) % 5.63/5.87 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota), % 5.63/5.87 Or (Eq (big_p a) False) % 5.63/5.87 (Or (Eq (Not (big_p (skS.0 1 a_1))) True) (Eq (Iff (big_p a_2) (big_p (skS.0 0 a_2 a_3))) False)) % 5.63/5.87 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota), % 5.63/5.87 Or (Eq (big_p a) False) (Or (Eq (Iff (big_p a_1) (big_p (skS.0 0 a_1 a_2))) False) (Eq (big_p (skS.0 1 a_3)) False)) % 5.63/5.87 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), % 5.63/5.87 Or (Eq (big_p a) False) % 5.63/5.87 (Or (Eq (big_p (skS.0 1 a_1)) False) (Or (Eq (big_p a_2) False) (Eq (big_p (skS.0 0 a_2 a_3)) False))) % 5.63/5.87 Clause #15 (by clausification #[7]): ∀ (a a_1 : Iota), % 5.63/5.87 Or (Eq (Exists big_p) True) % 5.63/5.87 (Or (Eq (∀ (Y : Iota), big_p Y) True) (Eq (Not (Iff (big_p a) (big_p (skS.0 2 a a_1)))) True)) % 5.63/5.87 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), % 5.63/5.87 Or (Eq (∀ (Y : Iota), big_p Y) True) % 5.63/5.87 (Or (Eq (Not (Iff (big_p a) (big_p (skS.0 2 a a_1)))) True) (Eq (big_p (skS.0 3 a_2)) True)) % 5.63/5.87 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 a_3 : Iota), % 5.63/5.87 Or (Eq (Not (Iff (big_p a) (big_p (skS.0 2 a a_1)))) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Eq (big_p a_3) True)) % 5.63/5.87 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota), % 5.63/5.87 Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Eq (Iff (big_p a_2) (big_p (skS.0 2 a_2 a_3))) False)) % 5.63/5.87 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 a_3 : Iota), % 5.63/5.87 Or (Eq (big_p (skS.0 3 a)) True) % 5.63/5.87 (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Eq (big_p (skS.0 2 a_2 a_3)) True))) % 5.63/5.87 Clause #21 (by clausification #[4]): ∀ (a : Iota), % 5.63/5.87 Or (Eq (Iff (Exists big_p) (∀ (Y : Iota), big_p Y)) True) (Eq (∀ (Y : Iota), Iff (big_p (skS.0 4 a)) (big_p Y)) True) % 5.63/5.87 Clause #23 (by clausification #[21]): ∀ (a : Iota), % 5.63/5.87 Or (Eq (∀ (Y : Iota), Iff (big_p (skS.0 4 a)) (big_p Y)) True) % 5.63/5.87 (Or (Eq (Exists big_p) False) (Eq (∀ (Y : Iota), big_p Y) True)) % 5.63/5.87 Clause #30 (by clausification #[23]): ∀ (a a_1 : Iota), % 5.63/5.87 Or (Eq (Exists big_p) False) (Or (Eq (∀ (Y : Iota), big_p Y) True) (Eq (Iff (big_p (skS.0 4 a)) (big_p a_1)) True)) % 5.63/5.87 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), % 5.74/5.90 Or (Eq (∀ (Y : Iota), big_p Y) True) (Or (Eq (Iff (big_p (skS.0 4 a)) (big_p a_1)) True) (Eq (big_p a_2) False)) % 5.74/5.90 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), % 5.74/5.90 Or (Eq (Iff (big_p (skS.0 4 a)) (big_p a_1)) True) (Or (Eq (big_p a_2) False) (Eq (big_p a_3) True)) % 5.74/5.90 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota), % 5.74/5.90 Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) True) (Eq (big_p a_3) False))) % 5.74/5.90 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota), % 5.74/5.90 Or (Eq (big_p a) False) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) False) (Eq (big_p a_3) True))) % 5.74/5.90 Clause #51 (by equality factoring #[20]): ∀ (a a_1 a_2 : Iota), % 5.74/5.90 Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Or (Ne True True) (Eq (big_p (skS.0 2 a_1 a_2)) True))) % 5.74/5.90 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 5.74/5.90 Or (Eq (big_p (skS.0 3 a)) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 2 a_1 a_2)) True) (Or (Eq True False) (Eq True False)))) % 5.74/5.90 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 5.74/5.90 Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 2 a_1 a_2)) True) (Eq True False))) % 5.74/5.90 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Eq (big_p (skS.0 2 a_1 a_2)) True)) % 5.74/5.90 Clause #63 (by superposition #[55, 33]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.74/5.90 Or (Eq (big_p (skS.0 3 a)) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) % 5.74/5.90 (Or (Eq True False) (Or (Eq (big_p a_2) True) (Or (Eq (big_p (skS.0 4 a_3)) True) (Eq (big_p a_4) False))))) % 5.74/5.90 Clause #74 (by clausification #[63]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.74/5.90 Or (Eq (big_p (skS.0 3 a)) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Or (Eq (big_p (skS.0 4 a_3)) True) (Eq (big_p a_4) False)))) % 5.74/5.90 Clause #78 (by superposition #[74, 55]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.74/5.90 Or (Eq (big_p (skS.0 3 a)) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) % 5.74/5.90 (Or (Eq (big_p a_2) True) % 5.74/5.90 (Or (Eq (big_p (skS.0 4 a_3)) True) % 5.74/5.90 (Or (Eq (big_p (skS.0 3 a_4)) True) (Or (Eq (big_p a_5) True) (Eq False True)))))) % 5.74/5.90 Clause #110 (by clausification #[78]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 5.74/5.90 Or (Eq (big_p (skS.0 3 a)) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) % 5.74/5.90 (Or (Eq (big_p a_2) True) % 5.74/5.90 (Or (Eq (big_p (skS.0 4 a_3)) True) (Or (Eq (big_p (skS.0 3 a_4)) True) (Eq (big_p a_5) True))))) % 5.74/5.90 Clause #175 (by equality factoring #[110]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.74/5.90 Or (Eq (big_p a) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) % 5.74/5.90 (Or (Eq (big_p (skS.0 4 a_2)) True) % 5.74/5.90 (Or (Eq (big_p a_3) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_4)) True))))) % 5.74/5.90 Clause #183 (by clausification #[175]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.74/5.90 Or (Eq (big_p a) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) % 5.74/5.90 (Or (Eq (big_p (skS.0 4 a_2)) True) % 5.74/5.90 (Or (Eq (big_p a_3) True) (Or (Eq (big_p (skS.0 3 a_4)) True) (Or (Eq True False) (Eq True False)))))) % 5.74/5.90 Clause #185 (by clausification #[183]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.74/5.90 Or (Eq (big_p a) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) % 5.74/5.90 (Or (Eq (big_p (skS.0 4 a_2)) True) % 5.74/5.90 (Or (Eq (big_p a_3) True) (Or (Eq (big_p (skS.0 3 a_4)) True) (Eq True False))))) % 5.74/5.90 Clause #186 (by clausification #[185]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.74/5.90 Or (Eq (big_p a) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) % 5.74/5.90 (Or (Eq (big_p (skS.0 4 a_2)) True) (Or (Eq (big_p a_3) True) (Eq (big_p (skS.0 3 a_4)) True)))) % 5.74/5.90 Clause #245 (by equality factoring #[186]): ∀ (a a_1 a_2 a_3 : Iota), % 5.74/5.90 Or (Eq (big_p a) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_3)) True)))) % 5.74/5.90 Clause #246 (by clausification #[245]): ∀ (a a_1 a_2 a_3 : Iota), % 5.74/5.90 Or (Eq (big_p a) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) % 5.74/5.90 (Or (Eq (big_p (skS.0 4 a_2)) True) (Or (Eq (big_p (skS.0 3 a_3)) True) (Or (Eq True False) (Eq True False))))) % 5.74/5.90 Clause #248 (by clausification #[246]): ∀ (a a_1 a_2 a_3 : Iota), % 5.74/5.90 Or (Eq (big_p a) True) % 5.74/5.90 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) True) (Or (Eq (big_p (skS.0 3 a_3)) True) (Eq True False)))) % 5.77/5.94 Clause #249 (by clausification #[248]): ∀ (a a_1 a_2 a_3 : Iota), % 5.77/5.94 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) True) (Eq (big_p (skS.0 3 a_3)) True))) % 5.77/5.94 Clause #290 (by equality factoring #[249]): ∀ (a a_1 a_2 : Iota), % 5.77/5.94 Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_2)) True))) % 5.77/5.94 Clause #291 (by clausification #[290]): ∀ (a a_1 a_2 : Iota), % 5.77/5.94 Or (Eq (big_p a) True) % 5.77/5.94 (Or (Eq (big_p (skS.0 4 a_1)) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Or (Eq True False) (Eq True False)))) % 5.77/5.94 Clause #293 (by clausification #[291]): ∀ (a a_1 a_2 : Iota), % 5.77/5.94 Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Eq True False))) % 5.77/5.94 Clause #294 (by clausification #[293]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Eq (big_p (skS.0 3 a_2)) True)) % 5.77/5.94 Clause #331 (by equality factoring #[294]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_1)) True)) % 5.77/5.94 Clause #332 (by clausification #[331]): ∀ (a a_1 : Iota), % 5.77/5.94 Or (Eq (big_p (skS.0 4 a)) True) (Or (Eq (big_p (skS.0 3 a_1)) True) (Or (Eq True False) (Eq True False))) % 5.77/5.94 Clause #334 (by clausification #[332]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Or (Eq (big_p (skS.0 3 a_1)) True) (Eq True False)) % 5.77/5.94 Clause #335 (by clausification #[334]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Eq (big_p (skS.0 3 a_1)) True) % 5.77/5.94 Clause #343 (by superposition #[335, 34]): ∀ (a a_1 a_2 a_3 : Iota), % 5.77/5.94 Or (Eq (big_p (skS.0 3 a)) True) % 5.77/5.94 (Or (Eq True False) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) False) (Eq (big_p a_3) True)))) % 5.77/5.94 Clause #399 (by clausification #[343]): ∀ (a a_1 a_2 a_3 : Iota), % 5.77/5.94 Or (Eq (big_p (skS.0 3 a)) True) % 5.77/5.94 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 4 a_2)) False) (Eq (big_p a_3) True))) % 5.77/5.94 Clause #400 (by superposition #[399, 335]): ∀ (a a_1 a_2 a_3 : Iota), % 5.77/5.94 Or (Eq (big_p (skS.0 3 a)) True) % 5.77/5.94 (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Or (Eq False True) (Eq (big_p (skS.0 3 a_3)) True)))) % 5.77/5.94 Clause #402 (by clausification #[400]): ∀ (a a_1 a_2 a_3 : Iota), % 5.77/5.94 Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p a_2) True) (Eq (big_p (skS.0 3 a_3)) True))) % 5.77/5.94 Clause #429 (by equality factoring #[402]): ∀ (a a_1 a_2 : Iota), % 5.77/5.94 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_2)) True))) % 5.77/5.94 Clause #432 (by clausification #[429]): ∀ (a a_1 a_2 : Iota), % 5.77/5.94 Or (Eq (big_p a) True) % 5.77/5.94 (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Or (Eq True False) (Eq True False)))) % 5.77/5.94 Clause #434 (by clausification #[432]): ∀ (a a_1 a_2 : Iota), % 5.77/5.94 Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Or (Eq (big_p (skS.0 3 a_2)) True) (Eq True False))) % 5.77/5.94 Clause #435 (by clausification #[434]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p a_1) True) (Eq (big_p (skS.0 3 a_2)) True)) % 5.77/5.94 Clause #453 (by equality factoring #[435]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Ne True True) (Eq (big_p (skS.0 3 a_1)) True)) % 5.77/5.94 Clause #454 (by clausification #[453]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 3 a_1)) True) (Or (Eq True False) (Eq True False))) % 5.77/5.94 Clause #456 (by clausification #[454]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 3 a_1)) True) (Eq True False)) % 5.77/5.94 Clause #457 (by clausification #[456]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p (skS.0 3 a_1)) True) % 5.77/5.94 Clause #474 (by equality factoring #[457]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 3 a)) True) % 5.77/5.94 Clause #475 (by clausification #[474]): ∀ (a : Iota), Or (Eq (big_p (skS.0 3 a)) True) (Or (Eq True False) (Eq True False)) % 5.77/5.94 Clause #477 (by clausification #[475]): ∀ (a : Iota), Or (Eq (big_p (skS.0 3 a)) True) (Eq True False) % 5.77/5.94 Clause #478 (by clausification #[477]): ∀ (a : Iota), Eq (big_p (skS.0 3 a)) True % 5.77/5.94 Clause #479 (by superposition #[478, 13]): ∀ (a a_1 a_2 : Iota), % 5.77/5.96 Or (Eq True False) % 5.77/5.96 (Or (Eq (big_p (skS.0 1 a)) False) (Or (Eq (big_p a_1) False) (Eq (big_p (skS.0 0 a_1 a_2)) False))) % 5.77/5.96 Clause #480 (by superposition #[478, 33]): ∀ (a a_1 a_2 : Iota), % 5.77/5.96 Or (Eq True False) (Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Eq (big_p a_2) False))) % 5.77/5.96 Clause #481 (by superposition #[478, 34]): ∀ (a a_1 a_2 : Iota), % 5.77/5.96 Or (Eq True False) (Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) False) (Eq (big_p a_2) True))) % 5.77/5.96 Clause #491 (by clausification #[481]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) False) (Eq (big_p a_2) True)) % 5.77/5.96 Clause #493 (by clausification #[480]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Eq (big_p a_2) False)) % 5.77/5.96 Clause #494 (by superposition #[493, 478]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq (big_p (skS.0 4 a_1)) True) (Eq False True)) % 5.77/5.96 Clause #495 (by clausification #[494]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p (skS.0 4 a_1)) True) % 5.77/5.96 Clause #500 (by equality factoring #[495]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 4 a)) True) % 5.77/5.96 Clause #501 (by clausification #[500]): ∀ (a : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Or (Eq True False) (Eq True False)) % 5.77/5.96 Clause #503 (by clausification #[501]): ∀ (a : Iota), Or (Eq (big_p (skS.0 4 a)) True) (Eq True False) % 5.77/5.96 Clause #504 (by clausification #[503]): ∀ (a : Iota), Eq (big_p (skS.0 4 a)) True % 5.77/5.96 Clause #505 (by superposition #[504, 491]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Or (Eq True False) (Eq (big_p a_1) True)) % 5.77/5.96 Clause #506 (by clausification #[505]): ∀ (a a_1 : Iota), Or (Eq (big_p a) True) (Eq (big_p a_1) True) % 5.77/5.96 Clause #507 (by equality factoring #[506]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p a) True) % 5.77/5.96 Clause #508 (by clausification #[507]): ∀ (a : Iota), Or (Eq (big_p a) True) (Or (Eq True False) (Eq True False)) % 5.77/5.96 Clause #510 (by clausification #[508]): ∀ (a : Iota), Or (Eq (big_p a) True) (Eq True False) % 5.77/5.96 Clause #511 (by clausification #[510]): ∀ (a : Iota), Eq (big_p a) True % 5.77/5.96 Clause #538 (by clausification #[479]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Or (Eq (big_p a_1) False) (Eq (big_p (skS.0 0 a_1 a_2)) False)) % 5.77/5.96 Clause #539 (by forward demodulation #[538, 511]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Or (Eq True False) (Eq (big_p (skS.0 0 a_1 a_2)) False)) % 5.77/5.96 Clause #540 (by clausification #[539]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p (skS.0 1 a)) False) (Eq (big_p (skS.0 0 a_1 a_2)) False) % 5.77/5.96 Clause #541 (by superposition #[540, 511]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 0 a a_1)) False) (Eq False True) % 5.77/5.96 Clause #542 (by clausification #[541]): ∀ (a a_1 : Iota), Eq (big_p (skS.0 0 a a_1)) False % 5.77/5.96 Clause #543 (by superposition #[542, 511]): Eq False True % 5.77/5.96 Clause #546 (by clausification #[543]): False % 5.77/5.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------