%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN347+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:07:27 PM UTC 2025 % Result : Theorem 4.24s 4.44s % Output : Proof 4.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYN347+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.15 % Command : duper %s % 0.14/0.34 % Computer : n011.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 15:18:53 EDT 2025 % 0.14/0.34 % CPUTime : % 4.24/4.44 SZS status Theorem for theBenchmark.p % 4.24/4.44 SZS output start Proof for theBenchmark.p % 4.24/4.44 Clause #0 (by assumption #[]): Eq % 4.24/4.44 (Not % 4.24/4.44 (∀ (Z1 Z2 : Iota), % 4.24/4.44 Exists fun X1 => % 4.24/4.44 Exists fun X2 => % 4.24/4.44 ∀ (Y : Iota), Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f Z1 Z2)) (Iff (big_f Z1 Y) (big_f Z2 Y)))) % 4.24/4.44 True % 4.24/4.44 Clause #1 (by clausification #[0]): Eq % 4.24/4.44 (∀ (Z1 Z2 : Iota), % 4.24/4.44 Exists fun X1 => % 4.24/4.44 Exists fun X2 => % 4.24/4.44 ∀ (Y : Iota), Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f Z1 Z2)) (Iff (big_f Z1 Y) (big_f Z2 Y))) % 4.24/4.44 False % 4.24/4.44 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 4.24/4.44 Eq % 4.24/4.44 (Not % 4.24/4.44 (∀ (Z2 : Iota), % 4.24/4.44 Exists fun X1 => % 4.24/4.44 Exists fun X2 => % 4.24/4.44 ∀ (Y : Iota), % 4.24/4.44 Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f (skS.0 0 a) Z2)) (Iff (big_f (skS.0 0 a) Y) (big_f Z2 Y)))) % 4.24/4.44 True % 4.24/4.44 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 4.24/4.44 Eq % 4.24/4.44 (∀ (Z2 : Iota), % 4.24/4.44 Exists fun X1 => % 4.24/4.44 Exists fun X2 => % 4.24/4.44 ∀ (Y : Iota), % 4.24/4.44 Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f (skS.0 0 a) Z2)) (Iff (big_f (skS.0 0 a) Y) (big_f Z2 Y))) % 4.24/4.44 False % 4.24/4.44 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 4.24/4.44 Eq % 4.24/4.44 (Not % 4.24/4.44 (Exists fun X1 => % 4.24/4.44 Exists fun X2 => % 4.24/4.44 ∀ (Y : Iota), % 4.24/4.44 Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.44 (Iff (big_f (skS.0 0 a) Y) (big_f (skS.0 1 a a_1) Y)))) % 4.24/4.44 True % 4.24/4.44 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 4.24/4.44 Eq % 4.24/4.44 (Exists fun X1 => % 4.24/4.44 Exists fun X2 => % 4.24/4.44 ∀ (Y : Iota), % 4.24/4.44 Or (Iff (Iff (big_f X1 Y) (big_f X2 Y)) (big_f (skS.0 0 a) (skS.0 1 a a_1))) % 4.24/4.44 (Iff (big_f (skS.0 0 a) Y) (big_f (skS.0 1 a a_1) Y))) % 4.24/4.44 False % 4.24/4.44 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 4.24/4.44 Eq % 4.24/4.44 (Exists fun X2 => % 4.24/4.44 ∀ (Y : Iota), % 4.24/4.44 Or (Iff (Iff (big_f a Y) (big_f X2 Y)) (big_f (skS.0 0 a_1) (skS.0 1 a_1 a_2))) % 4.24/4.44 (Iff (big_f (skS.0 0 a_1) Y) (big_f (skS.0 1 a_1 a_2) Y))) % 4.24/4.44 False % 4.24/4.44 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), % 4.24/4.44 Eq % 4.24/4.44 (∀ (Y : Iota), % 4.24/4.44 Or (Iff (Iff (big_f a Y) (big_f a_1 Y)) (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3))) % 4.24/4.44 (Iff (big_f (skS.0 0 a_2) Y) (big_f (skS.0 1 a_2 a_3) Y))) % 4.24/4.44 False % 4.24/4.44 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.44 Eq % 4.24/4.44 (Not % 4.24/4.44 (Or % 4.24/4.44 (Iff (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4))) % 4.24/4.44 (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3))) % 4.24/4.44 (Iff (big_f (skS.0 0 a_2) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f (skS.0 1 a_2 a_3) (skS.0 2 a a_1 a_2 a_3 a_4))))) % 4.24/4.44 True % 4.24/4.44 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.44 Eq % 4.24/4.44 (Or % 4.24/4.44 (Iff (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4))) % 4.24/4.44 (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3))) % 4.24/4.44 (Iff (big_f (skS.0 0 a_2) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f (skS.0 1 a_2 a_3) (skS.0 2 a a_1 a_2 a_3 a_4)))) % 4.24/4.44 False % 4.24/4.44 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.44 Eq (Iff (big_f (skS.0 0 a) (skS.0 2 a_1 a_2 a a_3 a_4)) (big_f (skS.0 1 a a_3) (skS.0 2 a_1 a_2 a a_3 a_4))) False % 4.24/4.44 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.44 Eq % 4.24/4.44 (Iff (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4))) % 4.24/4.44 (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3))) % 4.24/4.44 False % 4.24/4.44 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.44 Or (Eq (big_f (skS.0 0 a) (skS.0 2 a_1 a_2 a a_3 a_4)) False) % 4.24/4.44 (Eq (big_f (skS.0 1 a a_3) (skS.0 2 a_1 a_2 a a_3 a_4)) False) % 4.24/4.44 Clause #13 (by clausification #[10]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.44 Or (Eq (big_f (skS.0 0 a) (skS.0 2 a_1 a_2 a a_3 a_4)) True) % 4.24/4.44 (Eq (big_f (skS.0 1 a a_3) (skS.0 2 a_1 a_2 a a_3 a_4)) True) % 4.24/4.44 Clause #14 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.44 Or (Eq (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4))) False) % 4.24/4.44 (Eq (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3)) False) % 4.24/4.44 Clause #15 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.24/4.44 Or (Eq (Iff (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4))) True) % 4.28/4.47 (Eq (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3)) True) % 4.28/4.47 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False) % 4.28/4.47 (Or (Eq (big_f a_2 (skS.0 2 a_2 a_3 a a_1 a_4)) False) (Eq (big_f a_3 (skS.0 2 a_2 a_3 a a_1 a_4)) False)) % 4.28/4.47 Clause #17 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False) % 4.28/4.47 (Or (Eq (big_f a_2 (skS.0 2 a_2 a_3 a a_1 a_4)) True) (Eq (big_f a_3 (skS.0 2 a_2 a_3 a a_1 a_4)) True)) % 4.28/4.47 Clause #18 (by clausification #[15]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq (big_f a_2 (skS.0 2 a_2 a_3 a a_1 a_4)) True) (Eq (big_f a_3 (skS.0 2 a_2 a_3 a a_1 a_4)) False)) % 4.28/4.47 Clause #19 (by clausification #[15]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq (big_f a_2 (skS.0 2 a_2 a_3 a a_1 a_4)) False) (Eq (big_f a_3 (skS.0 2 a_2 a_3 a a_1 a_4)) True)) % 4.28/4.47 Clause #21 (by superposition #[19, 13]): ∀ (a a_1 a_2 a_3 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq (big_f a_2 (skS.0 2 (skS.0 1 a a_1) a_2 a a_1 a_3)) True) % 4.28/4.47 (Or (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) a_2 a a_1 a_3)) True) (Eq False True))) % 4.28/4.47 Clause #34 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq (big_f a_2 (skS.0 2 (skS.0 1 a a_1) a_2 a a_1 a_3)) True) % 4.28/4.47 (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) a_2 a a_1 a_3)) True)) % 4.28/4.47 Clause #37 (by equality factoring #[34]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Ne True True) (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True)) % 4.28/4.47 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True) % 4.28/4.47 (Or (Eq True False) (Eq True False))) % 4.28/4.47 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True) (Eq True False)) % 4.28/4.47 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Eq (big_f (skS.0 0 a) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True) % 4.28/4.47 Clause #42 (by superposition #[41, 12]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq True False) (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) False)) % 4.28/4.47 Clause #43 (by superposition #[41, 18]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True) (Eq True False))) % 4.28/4.47 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) False) % 4.28/4.47 Clause #46 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True)) % 4.28/4.47 Clause #47 (by eliminate duplicate literals #[46]): ∀ (a a_1 a_2 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 (Eq (big_f (skS.0 1 a a_1) (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a a_1 a_2)) True) % 4.28/4.47 Clause #48 (by superposition #[47, 44]): ∀ (a a_1 : Iota), % 4.28/4.47 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq True False)) % 4.28/4.47 Clause #52 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True) % 4.28/4.47 Clause #53 (by eliminate duplicate literals #[52]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True % 4.28/4.48 Clause #61 (by superposition #[53, 16]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.28/4.48 Or (Eq True False) % 4.28/4.48 (Or (Eq (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) False) (Eq (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)) False)) % 4.28/4.48 Clause #62 (by superposition #[53, 17]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.28/4.48 Or (Eq True False) % 4.28/4.48 (Or (Eq (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) True) (Eq (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)) True)) % 4.28/4.48 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.28/4.48 Or (Eq (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) True) (Eq (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)) True) % 4.28/4.48 Clause #66 (by equality factoring #[63]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne True True) (Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) True) % 4.28/4.48 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) True) (Or (Eq True False) (Eq True False)) % 4.28/4.48 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) True) (Eq True False) % 4.28/4.48 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) True % 4.28/4.48 Clause #77 (by clausification #[61]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.28/4.48 Or (Eq (big_f a (skS.0 2 a a_1 a_2 a_3 a_4)) False) (Eq (big_f a_1 (skS.0 2 a a_1 a_2 a_3 a_4)) False) % 4.28/4.48 Clause #80 (by superposition #[77, 70]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) False) (Eq False True) % 4.28/4.48 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_f a (skS.0 2 a a a_1 a_2 a_3)) False % 4.28/4.48 Clause #83 (by superposition #[81, 70]): Eq False True % 4.28/4.48 Clause #87 (by clausification #[83]): False % 4.28/4.48 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------