%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN352+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:07:28 PM UTC 2025 % Result : Theorem 4.47s 4.64s % Output : Proof 4.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SYN352+1 : TPTP v9.2.0. Released v2.0.0. % 0.10/0.13 % Command : duper %s % 0.12/0.33 % Computer : n020.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 15:06:38 EDT 2025 % 0.12/0.34 % CPUTime : % 4.47/4.64 SZS status Theorem for theBenchmark.p % 4.47/4.64 SZS output start Proof for theBenchmark.p % 4.47/4.64 Clause #0 (by assumption #[]): Eq % 4.47/4.64 (Not % 4.47/4.64 (∀ (X1 X2 : Iota), % 4.47/4.64 Exists fun Y1 => % 4.47/4.64 Exists fun Y2 => % 4.47/4.64 ∀ (Z : Iota), % 4.47/4.64 big_f X1 X2 → % 4.47/4.64 (big_f Y1 Y2 → Or (big_f X2 Z) (big_f Y2 Z)) → % 4.47/4.64 ((big_f Y1 Y2 → Iff (big_f X2 Z) (big_f Y1 Z)) → big_f Z Z) → % 4.47/4.64 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z)))) % 4.47/4.64 True % 4.47/4.64 Clause #1 (by clausification #[0]): Eq % 4.47/4.64 (∀ (X1 X2 : Iota), % 4.47/4.64 Exists fun Y1 => % 4.47/4.64 Exists fun Y2 => % 4.47/4.64 ∀ (Z : Iota), % 4.47/4.64 big_f X1 X2 → % 4.47/4.64 (big_f Y1 Y2 → Or (big_f X2 Z) (big_f Y2 Z)) → % 4.47/4.64 ((big_f Y1 Y2 → Iff (big_f X2 Z) (big_f Y1 Z)) → big_f Z Z) → % 4.47/4.64 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z))) % 4.47/4.64 False % 4.47/4.64 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 4.47/4.64 Eq % 4.47/4.64 (Not % 4.47/4.64 (∀ (X2 : Iota), % 4.47/4.64 Exists fun Y1 => % 4.47/4.64 Exists fun Y2 => % 4.47/4.64 ∀ (Z : Iota), % 4.47/4.64 big_f (skS.0 0 a) X2 → % 4.47/4.64 (big_f Y1 Y2 → Or (big_f X2 Z) (big_f Y2 Z)) → % 4.47/4.64 ((big_f Y1 Y2 → Iff (big_f X2 Z) (big_f Y1 Z)) → big_f Z Z) → % 4.47/4.64 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z)))) % 4.47/4.64 True % 4.47/4.64 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 4.47/4.64 Eq % 4.47/4.64 (∀ (X2 : Iota), % 4.47/4.64 Exists fun Y1 => % 4.47/4.64 Exists fun Y2 => % 4.47/4.64 ∀ (Z : Iota), % 4.47/4.64 big_f (skS.0 0 a) X2 → % 4.47/4.64 (big_f Y1 Y2 → Or (big_f X2 Z) (big_f Y2 Z)) → % 4.47/4.64 ((big_f Y1 Y2 → Iff (big_f X2 Z) (big_f Y1 Z)) → big_f Z Z) → % 4.47/4.64 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z))) % 4.47/4.64 False % 4.47/4.64 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 4.47/4.64 Eq % 4.47/4.64 (Not % 4.47/4.64 (Exists fun Y1 => % 4.47/4.64 Exists fun Y2 => % 4.47/4.64 ∀ (Z : Iota), % 4.47/4.64 big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.47/4.64 (big_f Y1 Y2 → Or (big_f (skS.0 1 a a_1) Z) (big_f Y2 Z)) → % 4.47/4.64 ((big_f Y1 Y2 → Iff (big_f (skS.0 1 a a_1) Z) (big_f Y1 Z)) → big_f Z Z) → % 4.47/4.64 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z)))) % 4.47/4.64 True % 4.47/4.64 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 4.47/4.64 Eq % 4.47/4.64 (Exists fun Y1 => % 4.47/4.64 Exists fun Y2 => % 4.47/4.64 ∀ (Z : Iota), % 4.47/4.64 big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.47/4.64 (big_f Y1 Y2 → Or (big_f (skS.0 1 a a_1) Z) (big_f Y2 Z)) → % 4.47/4.64 ((big_f Y1 Y2 → Iff (big_f (skS.0 1 a a_1) Z) (big_f Y1 Z)) → big_f Z Z) → % 4.47/4.64 And (big_f Y1 Y2) (Iff (big_f Y1 Z) (big_f Y2 Z))) % 4.47/4.64 False % 4.47/4.64 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 4.47/4.64 Eq % 4.47/4.64 (Exists fun Y2 => % 4.47/4.64 ∀ (Z : Iota), % 4.47/4.64 big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.47/4.64 (big_f a_2 Y2 → Or (big_f (skS.0 1 a a_1) Z) (big_f Y2 Z)) → % 4.47/4.64 ((big_f a_2 Y2 → Iff (big_f (skS.0 1 a a_1) Z) (big_f a_2 Z)) → big_f Z Z) → % 4.47/4.64 And (big_f a_2 Y2) (Iff (big_f a_2 Z) (big_f Y2 Z))) % 4.47/4.64 False % 4.47/4.64 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), % 4.47/4.64 Eq % 4.47/4.64 (∀ (Z : Iota), % 4.47/4.64 big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.47/4.64 (big_f a_2 a_3 → Or (big_f (skS.0 1 a a_1) Z) (big_f a_3 Z)) → % 4.47/4.64 ((big_f a_2 a_3 → Iff (big_f (skS.0 1 a a_1) Z) (big_f a_2 Z)) → big_f Z Z) → % 4.47/4.64 And (big_f a_2 a_3) (Iff (big_f a_2 Z) (big_f a_3 Z))) % 4.47/4.64 False % 4.47/4.64 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.64 Eq % 4.47/4.64 (Not % 4.47/4.64 (big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.47/4.64 (big_f a_2 a_3 → % 4.47/4.64 Or (big_f (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_3 (skS.0 2 a a_1 a_2 a_3 a_4))) → % 4.47/4.64 ((big_f a_2 a_3 → % 4.47/4.64 Iff (big_f (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4))) → % 4.47/4.64 big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.47/4.64 And (big_f a_2 a_3) (Iff (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_3 (skS.0 2 a a_1 a_2 a_3 a_4))))) % 4.47/4.64 True % 4.47/4.64 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.64 Eq % 4.47/4.64 (big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.47/4.66 (big_f a_2 a_3 → Or (big_f (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_3 (skS.0 2 a a_1 a_2 a_3 a_4))) → % 4.47/4.66 ((big_f a_2 a_3 → % 4.47/4.66 Iff (big_f (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4))) → % 4.47/4.66 big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.47/4.66 And (big_f a_2 a_3) (Iff (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_3 (skS.0 2 a a_1 a_2 a_3 a_4)))) % 4.47/4.66 False % 4.47/4.66 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.66 Eq % 4.47/4.66 ((big_f a a_1 → Or (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4))) → % 4.47/4.66 ((big_f a a_1 → Iff (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a (skS.0 2 a_2 a_3 a a_1 a_4))) → % 4.47/4.66 big_f (skS.0 2 a_2 a_3 a a_1 a_4) (skS.0 2 a_2 a_3 a a_1 a_4)) → % 4.47/4.66 And (big_f a a_1) (Iff (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4)))) % 4.47/4.66 False % 4.47/4.66 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.66 Eq % 4.47/4.66 (((big_f a a_1 → Iff (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a (skS.0 2 a_2 a_3 a a_1 a_4))) → % 4.47/4.66 big_f (skS.0 2 a_2 a_3 a a_1 a_4) (skS.0 2 a_2 a_3 a a_1 a_4)) → % 4.47/4.66 And (big_f a a_1) (Iff (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4)))) % 4.47/4.66 False % 4.47/4.66 Clause #17 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.66 Eq % 4.47/4.66 ((big_f a a_1 → Iff (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a (skS.0 2 a_2 a_3 a a_1 a_4))) → % 4.47/4.66 big_f (skS.0 2 a_2 a_3 a a_1 a_4) (skS.0 2 a_2 a_3 a a_1 a_4)) % 4.47/4.66 True % 4.47/4.66 Clause #18 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.66 Eq (And (big_f a a_1) (Iff (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4)))) False % 4.47/4.66 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.66 Or % 4.47/4.66 (Eq (big_f a a_1 → Iff (big_f (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a (skS.0 2 a_2 a_3 a a_1 a_4))) % 4.47/4.66 False) % 4.47/4.66 (Eq (big_f (skS.0 2 a_2 a_3 a a_1 a_4) (skS.0 2 a_2 a_3 a a_1 a_4)) True) % 4.47/4.66 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.66 Or (Eq (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) True) (Eq (big_f a_2 a_3) True) % 4.47/4.66 Clause #23 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.66 Or (Eq (big_f a a_1) False) % 4.47/4.66 (Eq (Iff (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4))) False) % 4.47/4.66 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.66 Or (Eq (big_f a a_1) False) % 4.47/4.66 (Or (Eq (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) False) (Eq (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4)) False)) % 4.47/4.66 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.66 Or (Eq (big_f a a_1) False) % 4.47/4.66 (Or (Eq (big_f a (skS.0 2 a_2 a_3 a a_1 a_4)) True) (Eq (big_f a_1 (skS.0 2 a_2 a_3 a a_1 a_4)) True)) % 4.47/4.66 Clause #27 (by superposition #[24, 20]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.47/4.66 Or % 4.47/4.66 (Eq % 4.47/4.66 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.66 False) % 4.47/4.66 (Or % 4.47/4.66 (Eq % 4.47/4.66 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) % 4.47/4.66 (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.66 False) % 4.47/4.66 (Or (Eq False True) (Eq (big_f a_2 a_3) True))) % 4.47/4.66 Clause #29 (by superposition #[25, 20]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.47/4.66 Or % 4.47/4.66 (Eq % 4.47/4.66 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.66 True) % 4.47/4.66 (Or % 4.47/4.66 (Eq % 4.47/4.66 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) % 4.47/4.66 (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.66 True) % 4.47/4.66 (Or (Eq False True) (Eq (big_f a_2 a_3) True))) % 4.47/4.66 Clause #67 (by clausification #[29]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.47/4.66 Or % 4.47/4.66 (Eq % 4.47/4.66 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.66 True) % 4.47/4.66 (Or % 4.47/4.66 (Eq % 4.47/4.66 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) % 4.47/4.68 (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.68 True) % 4.47/4.68 (Eq (big_f a_2 a_3) True)) % 4.47/4.68 Clause #68 (by eliminate duplicate literals #[67]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.47/4.68 Or % 4.47/4.68 (Eq % 4.47/4.68 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.68 True) % 4.47/4.68 (Eq (big_f a_2 a_3) True) % 4.47/4.68 Clause #72 (by clausification #[27]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.47/4.68 Or % 4.47/4.68 (Eq % 4.47/4.68 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.68 False) % 4.47/4.68 (Or % 4.47/4.68 (Eq % 4.47/4.68 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) % 4.47/4.68 (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.68 False) % 4.47/4.68 (Eq (big_f a_2 a_3) True)) % 4.47/4.68 Clause #73 (by eliminate duplicate literals #[72]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.47/4.68 Or % 4.47/4.68 (Eq % 4.47/4.68 (big_f (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a_5 a_6 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4) a_7)) % 4.47/4.68 False) % 4.47/4.68 (Eq (big_f a_2 a_3) True) % 4.47/4.68 Clause #74 (by superposition #[73, 68]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq False True) (Eq (big_f a a_1) True)) % 4.47/4.68 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a a_1) True) % 4.47/4.68 Clause #76 (by eliminate duplicate literals #[75]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True % 4.47/4.68 Clause #84 (by backward demodulation #[76, 24]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.68 Or (Eq True False) % 4.47/4.68 (Or (Eq (big_f a (skS.0 2 a_1 a_2 a a_3 a_4)) False) (Eq (big_f a_3 (skS.0 2 a_1 a_2 a a_3 a_4)) False)) % 4.47/4.68 Clause #91 (by clausification #[84]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.47/4.68 Or (Eq (big_f a (skS.0 2 a_1 a_2 a a_3 a_4)) False) (Eq (big_f a_3 (skS.0 2 a_1 a_2 a a_3 a_4)) False) % 4.47/4.68 Clause #92 (by superposition #[91, 76]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (big_f a (skS.0 2 a_1 a_2 a_3 a a_4)) False) (Eq False True) % 4.47/4.68 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_f a (skS.0 2 a_1 a_2 a_3 a a_4)) False % 4.47/4.68 Clause #94 (by superposition #[93, 76]): Eq False True % 4.47/4.68 Clause #95 (by clausification #[94]): False % 4.47/4.68 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------