%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN070+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:07:07 PM UTC 2025 % Result : Theorem 5.31s 5.52s % Output : Proof 5.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYN070+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n001.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 15:29:23 EDT 2025 % 0.13/0.36 % CPUTime : % 5.31/5.52 SZS status Theorem for theBenchmark.p % 5.31/5.52 SZS output start Proof for theBenchmark.p % 5.31/5.52 Clause #0 (by assumption #[]): Eq (∀ (X Y : Iota), And (big_f X) (And (big_f Y) (big_h Y X) → big_g Y) → big_g X) True % 5.31/5.52 Clause #1 (by assumption #[]): Eq % 5.31/5.52 ((Exists fun X => And (big_f X) (Not (big_g X))) → % 5.31/5.52 Exists fun X1 => And (And (big_f X1) (Not (big_g X1))) (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j X1 Y)) % 5.31/5.52 True % 5.31/5.52 Clause #2 (by assumption #[]): Eq (∀ (X Y : Iota), And (And (big_f X) (big_f Y)) (big_h X Y) → Not (big_j Y X)) True % 5.31/5.52 Clause #3 (by assumption #[]): Eq (Not (∀ (X : Iota), big_f X → big_g X)) True % 5.31/5.52 Clause #4 (by clausification #[3]): Eq (∀ (X : Iota), big_f X → big_g X) False % 5.31/5.52 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (big_f (skS.0 0 a) → big_g (skS.0 0 a))) True % 5.31/5.52 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (big_f (skS.0 0 a) → big_g (skS.0 0 a)) False % 5.31/5.52 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (big_f (skS.0 0 a)) True % 5.31/5.52 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (big_g (skS.0 0 a)) False % 5.31/5.52 Clause #9 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (Y : Iota), And (big_f a) (And (big_f Y) (big_h Y a) → big_g Y) → big_g a) True % 5.31/5.52 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (And (big_f a) (And (big_f a_1) (big_h a_1 a) → big_g a_1) → big_g a) True % 5.31/5.52 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (And (big_f a) (And (big_f a_1) (big_h a_1 a) → big_g a_1)) False) (Eq (big_g a) True) % 5.31/5.52 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 5.31/5.52 Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (And (big_f a_1) (big_h a_1 a) → big_g a_1) False)) % 5.31/5.52 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (And (big_f a_1) (big_h a_1 a)) True)) % 5.31/5.52 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (big_g a_1) False)) % 5.31/5.52 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (big_h a_1 a) True)) % 5.31/5.52 Clause #16 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_f a) False) (Eq (big_f a_1) True)) % 5.31/5.52 Clause #18 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), And (And (big_f a) (big_f Y)) (big_h a Y) → Not (big_j Y a)) True % 5.31/5.52 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (And (And (big_f a) (big_f a_1)) (big_h a a_1) → Not (big_j a_1 a)) True % 5.31/5.52 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (And (And (big_f a) (big_f a_1)) (big_h a a_1)) False) (Eq (Not (big_j a_1 a)) True) % 5.31/5.52 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (Not (big_j a a_1)) True) (Or (Eq (And (big_f a_1) (big_f a)) False) (Eq (big_h a_1 a) False)) % 5.31/5.52 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (And (big_f a) (big_f a_1)) False) (Or (Eq (big_h a a_1) False) (Eq (big_j a_1 a) False)) % 5.31/5.52 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 5.31/5.52 Or (Eq (big_h a a_1) False) (Or (Eq (big_j a_1 a) False) (Or (Eq (big_f a) False) (Eq (big_f a_1) False))) % 5.31/5.52 Clause #24 (by superposition #[16, 7]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_f a_1) True) (Eq False True)) % 5.31/5.52 Clause #25 (by clausification #[1]): Or (Eq (Exists fun X => And (big_f X) (Not (big_g X))) False) % 5.31/5.52 (Eq % 5.31/5.52 (Exists fun X1 => And (And (big_f X1) (Not (big_g X1))) (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j X1 Y)) % 5.31/5.52 True) % 5.31/5.52 Clause #26 (by clausification #[25]): ∀ (a : Iota), % 5.31/5.52 Or % 5.31/5.52 (Eq % 5.31/5.52 (Exists fun X1 => % 5.31/5.52 And (And (big_f X1) (Not (big_g X1))) (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j X1 Y)) % 5.31/5.52 True) % 5.31/5.52 (Eq (And (big_f a) (Not (big_g a))) False) % 5.31/5.52 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), % 5.31/5.52 Or (Eq (And (big_f a) (Not (big_g a))) False) % 5.31/5.52 (Eq % 5.31/5.52 (And (And (big_f (skS.0 1 a_1)) (Not (big_g (skS.0 1 a_1)))) % 5.31/5.52 (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j (skS.0 1 a_1) Y)) % 5.31/5.52 True) % 5.31/5.52 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), % 5.37/5.58 Or % 5.37/5.58 (Eq % 5.37/5.58 (And (And (big_f (skS.0 1 a)) (Not (big_g (skS.0 1 a)))) % 5.37/5.58 (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j (skS.0 1 a) Y)) % 5.37/5.58 True) % 5.37/5.58 (Or (Eq (big_f a_1) False) (Eq (Not (big_g a_1)) False)) % 5.37/5.58 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), % 5.37/5.58 Or (Eq (big_f a) False) % 5.37/5.58 (Or (Eq (Not (big_g a)) False) (Eq (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j (skS.0 1 a_1) Y) True)) % 5.37/5.58 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), % 5.37/5.58 Or (Eq (big_f a) False) % 5.37/5.58 (Or (Eq (∀ (Y : Iota), And (big_f Y) (Not (big_g Y)) → big_j (skS.0 1 a_1) Y) True) (Eq (big_g a) True)) % 5.37/5.58 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 5.37/5.58 Or (Eq (big_f a) False) % 5.37/5.58 (Or (Eq (big_g a) True) (Eq (And (big_f a_1) (Not (big_g a_1)) → big_j (skS.0 1 a_2) a_1) True)) % 5.37/5.58 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), % 5.37/5.58 Or (Eq (big_f a) False) % 5.37/5.58 (Or (Eq (big_g a) True) (Or (Eq (And (big_f a_1) (Not (big_g a_1))) False) (Eq (big_j (skS.0 1 a_2) a_1) True))) % 5.37/5.58 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 5.37/5.58 Or (Eq (big_f a) False) % 5.37/5.58 (Or (Eq (big_g a) True) % 5.37/5.58 (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq (big_f a_2) False) (Eq (Not (big_g a_2)) False)))) % 5.37/5.58 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 5.37/5.58 Or (Eq (big_f a) False) % 5.37/5.58 (Or (Eq (big_g a) True) (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq (big_f a_2) False) (Eq (big_g a_2) True)))) % 5.37/5.58 Clause #36 (by superposition #[35, 7]): ∀ (a a_1 a_2 : Iota), % 5.37/5.58 Or (Eq (big_g (skS.0 0 a)) True) % 5.37/5.58 (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq (big_f a_2) False) (Or (Eq (big_g a_2) True) (Eq False True)))) % 5.37/5.58 Clause #39 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Eq (big_f a_1) True) % 5.37/5.58 Clause #40 (by superposition #[39, 8]): ∀ (a : Iota), Or (Eq (big_f a) True) (Eq True False) % 5.37/5.58 Clause #46 (by clausification #[40]): ∀ (a : Iota), Eq (big_f a) True % 5.37/5.58 Clause #47 (by backward demodulation #[46, 15]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq True False) (Eq (big_h a_1 a) True)) % 5.37/5.58 Clause #48 (by backward demodulation #[46, 23]): ∀ (a a_1 : Iota), Or (Eq (big_h a a_1) False) (Or (Eq (big_j a_1 a) False) (Or (Eq True False) (Eq (big_f a_1) False))) % 5.37/5.58 Clause #51 (by backward demodulation #[46, 14]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq True False) (Eq (big_g a_1) False)) % 5.37/5.58 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_g a_1) False) % 5.37/5.58 Clause #57 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_h a_1 a) True) % 5.37/5.58 Clause #58 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (big_h a a_1) False) (Or (Eq (big_j a_1 a) False) (Eq (big_f a_1) False)) % 5.37/5.58 Clause #59 (by forward demodulation #[58, 46]): ∀ (a a_1 : Iota), Or (Eq (big_h a a_1) False) (Or (Eq (big_j a_1 a) False) (Eq True False)) % 5.37/5.58 Clause #60 (by clausification #[59]): ∀ (a a_1 : Iota), Or (Eq (big_h a a_1) False) (Eq (big_j a_1 a) False) % 5.37/5.58 Clause #62 (by superposition #[60, 57]): ∀ (a a_1 : Iota), Or (Eq (big_j a a_1) False) (Or (Eq (big_g a) True) (Eq False True)) % 5.37/5.58 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq (big_j a a_1) False) (Eq (big_g a) True) % 5.37/5.58 Clause #77 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 5.37/5.58 Or (Eq (big_g (skS.0 0 a)) True) % 5.37/5.58 (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq (big_f a_2) False) (Eq (big_g a_2) True))) % 5.37/5.58 Clause #78 (by forward demodulation #[77, 46]): ∀ (a a_1 a_2 : Iota), % 5.37/5.58 Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Or (Eq True False) (Eq (big_g a_2) True))) % 5.37/5.58 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_j (skS.0 1 a_1) a_2) True) (Eq (big_g a_2) True)) % 5.37/5.58 Clause #80 (by superposition #[79, 8]): ∀ (a a_1 : Iota), Or (Eq (big_j (skS.0 1 a) a_1) True) (Or (Eq (big_g a_1) True) (Eq True False)) % 5.37/5.58 Clause #83 (by clausification #[80]): ∀ (a a_1 : Iota), Or (Eq (big_j (skS.0 1 a) a_1) True) (Eq (big_g a_1) True) % 5.37/5.58 Clause #84 (by superposition #[83, 63]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq True False) (Eq (big_g (skS.0 1 a_1)) True)) % 5.37/5.59 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_g (skS.0 1 a_1)) True) % 5.37/5.59 Clause #88 (by superposition #[85, 52]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Or (Eq (big_g a_1) True) (Eq True False)) % 5.37/5.59 Clause #90 (by clausification #[88]): ∀ (a a_1 : Iota), Or (Eq (big_g a) True) (Eq (big_g a_1) True) % 5.37/5.59 Clause #91 (by superposition #[90, 8]): ∀ (a : Iota), Or (Eq (big_g a) True) (Eq True False) % 5.37/5.59 Clause #95 (by clausification #[91]): ∀ (a : Iota), Eq (big_g a) True % 5.37/5.59 Clause #99 (by superposition #[95, 8]): Eq True False % 5.37/5.59 Clause #100 (by clausification #[99]): False % 5.37/5.59 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------