%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN349+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 08:07:27 PM UTC 2025 % Result : Theorem 6.47s 6.68s % Output : Proof 6.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.14 % Problem : SYN349+1 : TPTP v9.2.0. Released v2.0.0. % 0.03/0.15 % Command : duper %s % 0.13/0.36 % Computer : n020.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Thu Oct 2 15:29:08 EDT 2025 % 0.13/0.36 % CPUTime : % 6.47/6.68 SZS status Theorem for theBenchmark.p % 6.47/6.68 SZS output start Proof for theBenchmark.p % 6.47/6.68 Clause #0 (by assumption #[]): Eq % 6.47/6.68 (Not % 6.47/6.68 (Exists fun X1 => % 6.47/6.68 ∀ (X2 : Iota), % 6.47/6.68 Exists fun X3 => % 6.47/6.68 ∀ (X4 : Iota), % 6.47/6.68 Iff (big_f X1 X4) (big_f X2 X4) → Iff (Iff (Iff (big_f X1 X4) (big_f X4 X3)) (big_f X3 X4)) (big_f X4 X2))) % 6.47/6.68 True % 6.47/6.68 Clause #1 (by clausification #[0]): Eq % 6.47/6.68 (Exists fun X1 => % 6.47/6.68 ∀ (X2 : Iota), % 6.47/6.68 Exists fun X3 => % 6.47/6.68 ∀ (X4 : Iota), % 6.47/6.68 Iff (big_f X1 X4) (big_f X2 X4) → Iff (Iff (Iff (big_f X1 X4) (big_f X4 X3)) (big_f X3 X4)) (big_f X4 X2)) % 6.47/6.68 False % 6.47/6.68 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 6.47/6.68 Eq % 6.47/6.68 (∀ (X2 : Iota), % 6.47/6.68 Exists fun X3 => % 6.47/6.68 ∀ (X4 : Iota), % 6.47/6.68 Iff (big_f a X4) (big_f X2 X4) → Iff (Iff (Iff (big_f a X4) (big_f X4 X3)) (big_f X3 X4)) (big_f X4 X2)) % 6.47/6.68 False % 6.47/6.68 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), % 6.47/6.68 Eq % 6.47/6.68 (Not % 6.47/6.68 (Exists fun X3 => % 6.47/6.68 ∀ (X4 : Iota), % 6.47/6.68 Iff (big_f a X4) (big_f (skS.0 0 a a_1) X4) → % 6.47/6.68 Iff (Iff (Iff (big_f a X4) (big_f X4 X3)) (big_f X3 X4)) (big_f X4 (skS.0 0 a a_1)))) % 6.47/6.68 True % 6.47/6.68 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 6.47/6.68 Eq % 6.47/6.68 (Exists fun X3 => % 6.47/6.68 ∀ (X4 : Iota), % 6.47/6.68 Iff (big_f a X4) (big_f (skS.0 0 a a_1) X4) → % 6.47/6.68 Iff (Iff (Iff (big_f a X4) (big_f X4 X3)) (big_f X3 X4)) (big_f X4 (skS.0 0 a a_1))) % 6.47/6.68 False % 6.47/6.68 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 6.47/6.68 Eq % 6.47/6.68 (∀ (X4 : Iota), % 6.47/6.68 Iff (big_f a X4) (big_f (skS.0 0 a a_1) X4) → % 6.47/6.68 Iff (Iff (Iff (big_f a X4) (big_f X4 a_2)) (big_f a_2 X4)) (big_f X4 (skS.0 0 a a_1))) % 6.47/6.68 False % 6.47/6.68 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 a_3 : Iota), % 6.47/6.68 Eq % 6.47/6.68 (Not % 6.47/6.68 (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 a_2 a_3)) → % 6.47/6.68 Iff % 6.47/6.68 (Iff (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) a_2)) % 6.47/6.68 (big_f a_2 (skS.0 1 a a_1 a_2 a_3))) % 6.47/6.68 (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)))) % 6.47/6.68 True % 6.47/6.68 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), % 6.47/6.68 Eq % 6.47/6.68 (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 a_2 a_3)) → % 6.47/6.68 Iff % 6.47/6.68 (Iff (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) a_2)) % 6.47/6.68 (big_f a_2 (skS.0 1 a a_1 a_2 a_3))) % 6.47/6.68 (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1))) % 6.47/6.68 False % 6.47/6.68 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), % 6.47/6.68 Eq (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 a_2 a_3))) True % 6.47/6.68 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), % 6.47/6.68 Eq % 6.47/6.68 (Iff % 6.47/6.68 (Iff (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) a_2)) % 6.47/6.68 (big_f a_2 (skS.0 1 a a_1 a_2 a_3))) % 6.47/6.68 (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1))) % 6.47/6.68 False % 6.47/6.68 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 6.47/6.68 Or (Eq (big_f a (skS.0 1 a a_1 a_2 a_3)) True) (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 a_2 a_3)) False) % 6.47/6.68 Clause #11 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 6.47/6.68 Or (Eq (big_f a (skS.0 1 a a_1 a_2 a_3)) False) (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 a_2 a_3)) True) % 6.47/6.68 Clause #12 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 6.47/6.68 Or % 6.47/6.68 (Eq % 6.47/6.68 (Iff (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) a_2)) % 6.47/6.68 (big_f a_2 (skS.0 1 a a_1 a_2 a_3))) % 6.47/6.68 False) % 6.47/6.68 (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) False) % 6.47/6.68 Clause #13 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 6.47/6.68 Or % 6.47/6.68 (Eq % 6.47/6.68 (Iff (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) a_2)) % 6.47/6.68 (big_f a_2 (skS.0 1 a a_1 a_2 a_3))) % 6.47/6.68 True) % 6.47/6.68 (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) True) % 6.47/6.68 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), % 6.47/6.68 Or (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) False) % 6.47/6.68 (Or (Eq (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) a_2)) False) % 6.47/6.68 (Eq (big_f a_2 (skS.0 1 a a_1 a_2 a_3)) False)) % 6.47/6.68 Clause #15 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) False) % 6.57/6.74 (Or (Eq (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) a_2)) True) % 6.57/6.74 (Eq (big_f a_2 (skS.0 1 a a_1 a_2 a_3)) True)) % 6.57/6.74 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) False) % 6.57/6.74 (Or (Eq (big_f a_2 (skS.0 1 a a_1 a_2 a_3)) False) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 a_2 a_3)) False) (Eq (big_f (skS.0 1 a a_1 a_2 a_3) a_2) False))) % 6.57/6.74 Clause #18 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) False) % 6.57/6.74 (Or (Eq (big_f a_2 (skS.0 1 a a_1 a_2 a_3)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 a_2 a_3)) True) (Eq (big_f (skS.0 1 a a_1 a_2 a_3) a_2) False))) % 6.57/6.74 Clause #20 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) True) % 6.57/6.74 (Or (Eq (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) a_2)) True) % 6.57/6.74 (Eq (big_f a_2 (skS.0 1 a a_1 a_2 a_3)) False)) % 6.57/6.74 Clause #21 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) True) % 6.57/6.74 (Or (Eq (Iff (big_f a (skS.0 1 a a_1 a_2 a_3)) (big_f (skS.0 1 a a_1 a_2 a_3) a_2)) False) % 6.57/6.74 (Eq (big_f a_2 (skS.0 1 a a_1 a_2 a_3)) True)) % 6.57/6.74 Clause #23 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) True) % 6.57/6.74 (Or (Eq (big_f a_2 (skS.0 1 a a_1 a_2 a_3)) False) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 a_2 a_3)) False) (Eq (big_f (skS.0 1 a a_1 a_2 a_3) a_2) True))) % 6.57/6.74 Clause #25 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 1 a a_1 a_2 a_3) (skS.0 0 a a_1)) True) % 6.57/6.74 (Or (Eq (big_f a_2 (skS.0 1 a a_1 a_2 a_3)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 a_2 a_3)) True) (Eq (big_f (skS.0 1 a a_1 a_2 a_3) a_2) True))) % 6.57/6.74 Clause #29 (by equality factoring #[25]): ∀ (a a_1 a_2 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Ne True True) (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True))) % 6.57/6.74 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True) (Or (Eq True False) (Eq True False)))) % 6.57/6.74 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True) (Eq True False))) % 6.57/6.74 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True)) % 6.57/6.74 Clause #36 (by superposition #[34, 18]): ∀ (a a_1 a_2 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq True False) % 6.57/6.74 (Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) (Eq True False))))) % 6.57/6.74 Clause #41 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) (Eq True False)))) % 6.57/6.74 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 6.57/6.74 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.74 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.78 (Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.78 (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True))) % 6.57/6.78 Clause #43 (by eliminate duplicate literals #[42]): ∀ (a a_1 a_2 : Iota), % 6.57/6.78 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.78 (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.78 Clause #44 (by superposition #[43, 10]): ∀ (a a_1 a_2 : Iota), % 6.57/6.78 Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.78 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) (Eq True False)) % 6.57/6.78 Clause #49 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 6.57/6.78 Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.78 Clause #50 (by eliminate duplicate literals #[49]): ∀ (a a_1 a_2 : Iota), Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True % 6.57/6.78 Clause #52 (by superposition #[50, 11]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True) % 6.57/6.78 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) True % 6.57/6.78 Clause #57 (by superposition #[54, 23]): ∀ (a a_1 a_2 : Iota), % 6.57/6.78 Or (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True) % 6.57/6.78 (Or (Eq True False) % 6.57/6.78 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) % 6.57/6.78 (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True))) % 6.57/6.78 Clause #60 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 6.57/6.78 Or (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True) % 6.57/6.78 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) % 6.57/6.78 (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True)) % 6.57/6.78 Clause #61 (by eliminate duplicate literals #[60]): ∀ (a a_1 a_2 : Iota), % 6.57/6.78 Or (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True) % 6.57/6.78 (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) % 6.57/6.78 Clause #62 (by forward demodulation #[61, 50]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True) (Eq True False) % 6.57/6.78 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 1 a a_1 (skS.0 0 a a_1) a_2) (skS.0 0 a a_1)) True % 6.57/6.78 Clause #64 (by superposition #[63, 16]): ∀ (a a_1 a_2 : Iota), % 6.57/6.78 Or (Eq True False) % 6.57/6.78 (Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) % 6.57/6.78 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) (Eq True False))) % 6.57/6.78 Clause #67 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 6.57/6.78 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) % 6.57/6.78 (Or (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) (Eq True False)) % 6.57/6.78 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 6.57/6.78 Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) % 6.57/6.78 (Eq (big_f a (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) % 6.57/6.78 Clause #69 (by forward demodulation #[68, 50]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False) (Eq True False) % 6.57/6.78 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a a_1) (skS.0 1 a a_1 (skS.0 0 a a_1) a_2)) False % 6.57/6.78 Clause #71 (by superposition #[70, 54]): Eq False True % 6.57/6.78 Clause #72 (by clausification #[71]): False % 6.57/6.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------