%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN354+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 4.04s 4.21s % Output : Proof 4.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN354+1 : TPTP v9.2.0. Released v2.0.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n025.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 15:20:08 EDT 2025 % 0.12/0.34 % CPUTime : % 4.04/4.21 SZS status Theorem for theBenchmark.p % 4.04/4.21 SZS output start Proof for theBenchmark.p % 4.04/4.21 Clause #0 (by assumption #[]): Eq % 4.04/4.21 (Not % 4.04/4.21 (∀ (X1 X2 : Iota), % 4.04/4.21 Exists fun Y1 => % 4.04/4.21 Exists fun Y2 => % 4.04/4.21 ∀ (Z : Iota), % 4.04/4.21 big_f X1 X2 → % 4.04/4.21 big_g X1 X2 → % 4.04/4.21 (Iff (big_g X2 Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f X2 Y2) → % 4.04/4.21 Iff (big_g X2 Z) (big_g Y1 Z) → And (And (big_f X1 Y1) (big_f X2 Y1)) (big_f Y1 Y2))) % 4.04/4.21 True % 4.04/4.21 Clause #1 (by clausification #[0]): Eq % 4.04/4.21 (∀ (X1 X2 : Iota), % 4.04/4.21 Exists fun Y1 => % 4.04/4.21 Exists fun Y2 => % 4.04/4.21 ∀ (Z : Iota), % 4.04/4.21 big_f X1 X2 → % 4.04/4.21 big_g X1 X2 → % 4.04/4.21 (Iff (big_g X2 Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f X2 Y2) → % 4.04/4.21 Iff (big_g X2 Z) (big_g Y1 Z) → And (And (big_f X1 Y1) (big_f X2 Y1)) (big_f Y1 Y2)) % 4.04/4.21 False % 4.04/4.21 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 4.04/4.21 Eq % 4.04/4.21 (Not % 4.04/4.21 (∀ (X2 : Iota), % 4.04/4.21 Exists fun Y1 => % 4.04/4.21 Exists fun Y2 => % 4.04/4.21 ∀ (Z : Iota), % 4.04/4.21 big_f (skS.0 0 a) X2 → % 4.04/4.21 big_g (skS.0 0 a) X2 → % 4.04/4.21 (Iff (big_g X2 Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f X2 Y2) → % 4.04/4.21 Iff (big_g X2 Z) (big_g Y1 Z) → And (And (big_f (skS.0 0 a) Y1) (big_f X2 Y1)) (big_f Y1 Y2))) % 4.04/4.21 True % 4.04/4.21 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 4.04/4.21 Eq % 4.04/4.21 (∀ (X2 : Iota), % 4.04/4.21 Exists fun Y1 => % 4.04/4.21 Exists fun Y2 => % 4.04/4.21 ∀ (Z : Iota), % 4.04/4.21 big_f (skS.0 0 a) X2 → % 4.04/4.21 big_g (skS.0 0 a) X2 → % 4.04/4.21 (Iff (big_g X2 Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f X2 Y2) → % 4.04/4.21 Iff (big_g X2 Z) (big_g Y1 Z) → And (And (big_f (skS.0 0 a) Y1) (big_f X2 Y1)) (big_f Y1 Y2)) % 4.04/4.21 False % 4.04/4.21 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 4.04/4.21 Eq % 4.04/4.21 (Not % 4.04/4.21 (Exists fun Y1 => % 4.04/4.21 Exists fun Y2 => % 4.04/4.21 ∀ (Z : Iota), % 4.04/4.21 big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 big_g (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 (Iff (big_g (skS.0 1 a a_1) Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f (skS.0 1 a a_1) Y2) → % 4.04/4.21 Iff (big_g (skS.0 1 a a_1) Z) (big_g Y1 Z) → % 4.04/4.21 And (And (big_f (skS.0 0 a) Y1) (big_f (skS.0 1 a a_1) Y1)) (big_f Y1 Y2))) % 4.04/4.21 True % 4.04/4.21 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 4.04/4.21 Eq % 4.04/4.21 (Exists fun Y1 => % 4.04/4.21 Exists fun Y2 => % 4.04/4.21 ∀ (Z : Iota), % 4.04/4.21 big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 big_g (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 (Iff (big_g (skS.0 1 a a_1) Z) (big_g Y2 Z) → big_f Y1 Y2 → big_f (skS.0 1 a a_1) Y2) → % 4.04/4.21 Iff (big_g (skS.0 1 a a_1) Z) (big_g Y1 Z) → % 4.04/4.21 And (And (big_f (skS.0 0 a) Y1) (big_f (skS.0 1 a a_1) Y1)) (big_f Y1 Y2)) % 4.04/4.21 False % 4.04/4.21 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 4.04/4.21 Eq % 4.04/4.21 (Exists fun Y2 => % 4.04/4.21 ∀ (Z : Iota), % 4.04/4.21 big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 big_g (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 (Iff (big_g (skS.0 1 a a_1) Z) (big_g Y2 Z) → big_f a_2 Y2 → big_f (skS.0 1 a a_1) Y2) → % 4.04/4.21 Iff (big_g (skS.0 1 a a_1) Z) (big_g a_2 Z) → % 4.04/4.21 And (And (big_f (skS.0 0 a) a_2) (big_f (skS.0 1 a a_1) a_2)) (big_f a_2 Y2)) % 4.04/4.21 False % 4.04/4.21 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), % 4.04/4.21 Eq % 4.04/4.21 (∀ (Z : Iota), % 4.04/4.21 big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 big_g (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 (Iff (big_g (skS.0 1 a a_1) Z) (big_g a_2 Z) → big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) → % 4.04/4.21 Iff (big_g (skS.0 1 a a_1) Z) (big_g a_3 Z) → % 4.04/4.21 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2)) % 4.04/4.21 False % 4.04/4.21 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.21 Eq % 4.04/4.21 (Not % 4.04/4.21 (big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 big_g (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.21 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.21 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) → % 4.04/4.21 Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.23 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2))) % 4.04/4.23 True % 4.04/4.23 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Eq % 4.04/4.23 (big_f (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.23 big_g (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.23 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.23 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) → % 4.04/4.23 Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.23 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2)) % 4.04/4.23 False % 4.04/4.23 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) True % 4.04/4.23 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Eq % 4.04/4.23 (big_g (skS.0 0 a) (skS.0 1 a a_1) → % 4.04/4.23 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.23 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) → % 4.04/4.23 Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.23 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2)) % 4.04/4.23 False % 4.04/4.23 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Eq % 4.04/4.23 ((Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.23 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) → % 4.04/4.23 Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.23 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2)) % 4.04/4.23 False % 4.04/4.23 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Eq % 4.04/4.23 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.23 big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) % 4.04/4.23 True % 4.04/4.23 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Eq % 4.04/4.23 (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_3 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 4.04/4.23 And (And (big_f (skS.0 0 a) a_3) (big_f (skS.0 1 a a_1) a_3)) (big_f a_3 a_2)) % 4.04/4.23 False % 4.04/4.23 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Or (Eq (Iff (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4))) False) % 4.04/4.23 (Eq (big_f a_3 a_2 → big_f (skS.0 1 a a_1) a_2) True) % 4.04/4.23 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Or (Eq (big_f a a_1 → big_f (skS.0 1 a_2 a_3) a_1) True) % 4.04/4.23 (Or (Eq (big_g (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_1 a a_4)) False) % 4.04/4.23 (Eq (big_g a_1 (skS.0 2 a_2 a_3 a_1 a a_4)) False)) % 4.04/4.23 Clause #18 (by clausification #[16]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Or (Eq (big_f a a_1 → big_f (skS.0 1 a_2 a_3) a_1) True) % 4.04/4.23 (Or (Eq (big_g (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_1 a a_4)) True) % 4.04/4.23 (Eq (big_g a_1 (skS.0 2 a_2 a_3 a_1 a a_4)) True)) % 4.04/4.23 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) False) % 4.04/4.23 (Or (Eq (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) False) % 4.04/4.23 (Or (Eq (big_f a_3 a_2) False) (Eq (big_f (skS.0 1 a a_1) a_2) True))) % 4.04/4.23 Clause #21 (by clausification #[15]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (And (big_f (skS.0 0 a) a_1) (big_f (skS.0 1 a a_2) a_1)) (big_f a_1 a_3)) False % 4.04/4.23 Clause #24 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), % 4.04/4.23 Or (Eq (And (big_f (skS.0 0 a) a_1) (big_f (skS.0 1 a a_2) a_1)) False) (Eq (big_f a_1 a_3) False) % 4.04/4.23 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), % 4.04/4.23 Or (Eq (big_f a a_1) False) (Or (Eq (big_f (skS.0 0 a_2) a) False) (Eq (big_f (skS.0 1 a_2 a_3) a) False)) % 4.04/4.23 Clause #27 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.23 Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 a_2 a_3 a_4)) True) % 4.04/4.23 (Or (Eq (big_g a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) True) % 4.04/4.23 (Or (Eq (big_f a_3 a_2) False) (Eq (big_f (skS.0 1 a a_1) a_2) True))) % 4.04/4.23 Clause #28 (by superposition #[27, 10]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.25 Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a_2 a_3) (skS.0 0 a_2) a_4)) True) % 4.04/4.25 (Or (Eq (big_g (skS.0 1 a_2 a_3) (skS.0 2 a a_1 (skS.0 1 a_2 a_3) (skS.0 0 a_2) a_4)) True) % 4.04/4.25 (Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a_2 a_3)) True) (Eq False True))) % 4.04/4.25 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.04/4.25 Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a_2 a_3) (skS.0 0 a_2) a_4)) True) % 4.04/4.25 (Or (Eq (big_g (skS.0 1 a_2 a_3) (skS.0 2 a a_1 (skS.0 1 a_2 a_3) (skS.0 0 a_2) a_4)) True) % 4.04/4.25 (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a_2 a_3)) True)) % 4.04/4.25 Clause #33 (by equality factoring #[30]): ∀ (a a_1 a_2 : Iota), % 4.04/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 4.04/4.25 (Or (Ne True True) (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True)) % 4.04/4.25 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), % 4.04/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 4.04/4.25 (Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True) % 4.04/4.25 (Or (Eq True False) (Eq True False))) % 4.04/4.25 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 4.04/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 4.04/4.25 (Or (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True) (Eq True False)) % 4.04/4.25 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 4.04/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 4.04/4.25 (Eq (big_g (skS.0 1 a a_1) (skS.0 2 a a_1 (skS.0 1 a a_1) (skS.0 0 a) a_2)) True) % 4.04/4.25 Clause #38 (by superposition #[37, 19]): ∀ (a a_1 : Iota), % 4.04/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 4.04/4.25 (Or (Eq True False) % 4.04/4.25 (Or (Eq True False) % 4.04/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)))) % 4.04/4.25 Clause #42 (by clausification #[38]): ∀ (a a_1 : Iota), % 4.04/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 4.04/4.25 (Or (Eq True False) % 4.04/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True))) % 4.04/4.25 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), % 4.04/4.25 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 4.04/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True)) % 4.04/4.25 Clause #44 (by eliminate duplicate literals #[43]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1)) False) % 4.04/4.25 Clause #45 (by forward demodulation #[44, 10]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True) (Eq True False) % 4.04/4.25 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1)) True % 4.04/4.25 Clause #49 (by superposition #[46, 25]): ∀ (a a_1 a_2 a_3 : Iota), % 4.04/4.25 Or (Eq True False) % 4.04/4.25 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) False) (Eq (big_f (skS.0 1 a a_3) (skS.0 1 a_1 a_2)) False)) % 4.04/4.25 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), % 4.04/4.25 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a_2)) False) (Eq (big_f (skS.0 1 a a_3) (skS.0 1 a_1 a_2)) False) % 4.04/4.25 Clause #52 (by superposition #[51, 10]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_2)) False) (Eq False True) % 4.04/4.25 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_2)) False % 4.04/4.25 Clause #54 (by superposition #[53, 46]): Eq False True % 4.04/4.25 Clause #55 (by clausification #[54]): False % 4.04/4.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------