%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN345+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 6.52s 6.69s % Output : Proof 6.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SYN345+1 : TPTP v9.2.0. Released v2.0.0. % 0.10/0.12 % Command : duper %s % 0.12/0.32 % Computer : n027.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Thu Oct 2 15:32:38 EDT 2025 % 0.12/0.33 % CPUTime : % 6.52/6.69 SZS status Theorem for theBenchmark.p % 6.52/6.69 SZS output start Proof for theBenchmark.p % 6.52/6.69 Clause #0 (by assumption #[]): Eq % 6.52/6.69 (Not % 6.52/6.69 (∀ (X1 X2 : Iota), % 6.52/6.69 Exists fun Y1 => % 6.52/6.69 Exists fun Y2 => % 6.52/6.69 ∀ (Z : Iota), % 6.52/6.69 ((big_f X1 X2 Y1 → big_f Y2 Y1 Z) → big_f X1 X1 X2 → big_f X1 X2 X2) → % 6.52/6.69 ((big_f X2 Y1 Y2 → big_f Y1 Z Z) → big_f X1 X2 X2 → big_f X1 X1 X2) → % 6.52/6.69 big_f Y1 Y2 Z → And (big_f X2 X2 Y1) (Iff (big_f X1 X1 X2) (big_f X1 X2 X2)))) % 6.52/6.69 True % 6.52/6.69 Clause #1 (by clausification #[0]): Eq % 6.52/6.69 (∀ (X1 X2 : Iota), % 6.52/6.69 Exists fun Y1 => % 6.52/6.69 Exists fun Y2 => % 6.52/6.69 ∀ (Z : Iota), % 6.52/6.69 ((big_f X1 X2 Y1 → big_f Y2 Y1 Z) → big_f X1 X1 X2 → big_f X1 X2 X2) → % 6.52/6.69 ((big_f X2 Y1 Y2 → big_f Y1 Z Z) → big_f X1 X2 X2 → big_f X1 X1 X2) → % 6.52/6.69 big_f Y1 Y2 Z → And (big_f X2 X2 Y1) (Iff (big_f X1 X1 X2) (big_f X1 X2 X2))) % 6.52/6.69 False % 6.52/6.69 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 6.52/6.69 Eq % 6.52/6.69 (Not % 6.52/6.69 (∀ (X2 : Iota), % 6.52/6.69 Exists fun Y1 => % 6.52/6.69 Exists fun Y2 => % 6.52/6.69 ∀ (Z : Iota), % 6.52/6.69 ((big_f (skS.0 0 a) X2 Y1 → big_f Y2 Y1 Z) → big_f (skS.0 0 a) (skS.0 0 a) X2 → big_f (skS.0 0 a) X2 X2) → % 6.52/6.69 ((big_f X2 Y1 Y2 → big_f Y1 Z Z) → big_f (skS.0 0 a) X2 X2 → big_f (skS.0 0 a) (skS.0 0 a) X2) → % 6.52/6.69 big_f Y1 Y2 Z → % 6.52/6.69 And (big_f X2 X2 Y1) (Iff (big_f (skS.0 0 a) (skS.0 0 a) X2) (big_f (skS.0 0 a) X2 X2)))) % 6.52/6.69 True % 6.52/6.69 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 6.52/6.69 Eq % 6.52/6.69 (∀ (X2 : Iota), % 6.52/6.69 Exists fun Y1 => % 6.52/6.69 Exists fun Y2 => % 6.52/6.69 ∀ (Z : Iota), % 6.52/6.69 ((big_f (skS.0 0 a) X2 Y1 → big_f Y2 Y1 Z) → big_f (skS.0 0 a) (skS.0 0 a) X2 → big_f (skS.0 0 a) X2 X2) → % 6.52/6.69 ((big_f X2 Y1 Y2 → big_f Y1 Z Z) → big_f (skS.0 0 a) X2 X2 → big_f (skS.0 0 a) (skS.0 0 a) X2) → % 6.52/6.69 big_f Y1 Y2 Z → And (big_f X2 X2 Y1) (Iff (big_f (skS.0 0 a) (skS.0 0 a) X2) (big_f (skS.0 0 a) X2 X2))) % 6.52/6.69 False % 6.52/6.69 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 6.52/6.69 Eq % 6.52/6.69 (Not % 6.52/6.69 (Exists fun Y1 => % 6.52/6.69 Exists fun Y2 => % 6.52/6.69 ∀ (Z : Iota), % 6.52/6.69 ((big_f (skS.0 0 a) (skS.0 1 a a_1) Y1 → big_f Y2 Y1 Z) → % 6.52/6.69 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) → % 6.52/6.69 ((big_f (skS.0 1 a a_1) Y1 Y2 → big_f Y1 Z Z) → % 6.52/6.69 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) → % 6.52/6.69 big_f Y1 Y2 Z → % 6.52/6.69 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) Y1) % 6.52/6.69 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) % 6.52/6.69 (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))))) % 6.52/6.69 True % 6.52/6.69 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 6.52/6.69 Eq % 6.52/6.69 (Exists fun Y1 => % 6.52/6.69 Exists fun Y2 => % 6.52/6.69 ∀ (Z : Iota), % 6.52/6.69 ((big_f (skS.0 0 a) (skS.0 1 a a_1) Y1 → big_f Y2 Y1 Z) → % 6.52/6.69 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) → % 6.52/6.69 ((big_f (skS.0 1 a a_1) Y1 Y2 → big_f Y1 Z Z) → % 6.52/6.69 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) → % 6.52/6.69 big_f Y1 Y2 Z → % 6.52/6.69 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) Y1) % 6.52/6.69 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) % 6.52/6.69 (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)))) % 6.52/6.69 False % 6.52/6.69 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 6.52/6.69 Eq % 6.52/6.69 (Exists fun Y2 => % 6.52/6.69 ∀ (Z : Iota), % 6.52/6.69 ((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f Y2 a_2 Z) → % 6.52/6.69 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) → % 6.52/6.69 ((big_f (skS.0 1 a a_1) a_2 Y2 → big_f a_2 Z Z) → % 6.52/6.69 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) → % 6.52/6.69 big_f a_2 Y2 Z → % 6.52/6.69 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) % 6.52/6.75 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) % 6.52/6.75 (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)))) % 6.52/6.75 False % 6.52/6.75 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), % 6.52/6.75 Eq % 6.52/6.75 (∀ (Z : Iota), % 6.52/6.75 ((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 Z) → % 6.52/6.75 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) → % 6.52/6.75 ((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 Z Z) → % 6.52/6.75 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) → % 6.52/6.75 big_f a_2 a_3 Z → % 6.52/6.75 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) % 6.52/6.75 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)))) % 6.52/6.75 False % 6.52/6.75 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.52/6.75 Eq % 6.52/6.75 (Not % 6.52/6.75 (((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 6.52/6.75 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) → % 6.52/6.75 ((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) → % 6.52/6.75 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) → % 6.52/6.75 big_f a_2 a_3 (skS.0 2 a a_1 a_2 a_3 a_4) → % 6.52/6.75 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) % 6.52/6.75 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) % 6.52/6.75 (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))))) % 6.52/6.75 True % 6.52/6.75 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.52/6.75 Eq % 6.52/6.75 (((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 6.52/6.75 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) → % 6.52/6.75 ((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) → % 6.52/6.75 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) → % 6.52/6.75 big_f a_2 a_3 (skS.0 2 a a_1 a_2 a_3 a_4) → % 6.52/6.75 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) % 6.52/6.75 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)))) % 6.52/6.75 False % 6.52/6.75 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.52/6.75 Eq % 6.52/6.75 ((big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) → % 6.52/6.75 big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) % 6.52/6.75 True % 6.52/6.75 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.52/6.75 Eq % 6.52/6.75 (((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) → % 6.52/6.75 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) → % 6.52/6.75 big_f a_2 a_3 (skS.0 2 a a_1 a_2 a_3 a_4) → % 6.52/6.75 And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) % 6.52/6.75 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)))) % 6.52/6.75 False % 6.52/6.75 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.52/6.75 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) a_2 → big_f a_3 a_2 (skS.0 2 a a_1 a_2 a_3 a_4)) False) % 6.52/6.75 (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 6.52/6.75 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.52/6.75 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 6.52/6.75 (Eq (big_f a_2 a_3 (skS.0 2 a a_1 a_3 a_2 a_4)) False) % 6.52/6.75 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.52/6.75 Or (Eq (big_f a a_1 (skS.0 2 a_2 a_3 a_1 a a_4)) False) % 6.52/6.75 (Or (Eq (big_f (skS.0 0 a_2) (skS.0 0 a_2) (skS.0 1 a_2 a_3)) False) % 6.52/6.75 (Eq (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 1 a_2 a_3)) True)) % 6.52/6.75 Clause #17 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.62/6.81 Eq % 6.62/6.81 ((big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) → % 6.62/6.81 big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) % 6.62/6.81 True % 6.62/6.81 Clause #18 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.62/6.81 Eq % 6.62/6.81 (big_f a a_1 (skS.0 2 a_2 a_3 a a_1 a_4) → % 6.62/6.81 And (big_f (skS.0 1 a_2 a_3) (skS.0 1 a_2 a_3) a) % 6.62/6.81 (Iff (big_f (skS.0 0 a_2) (skS.0 0 a_2) (skS.0 1 a_2 a_3)) % 6.62/6.81 (big_f (skS.0 0 a_2) (skS.0 1 a_2 a_3) (skS.0 1 a_2 a_3)))) % 6.62/6.81 False % 6.62/6.81 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3 → big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) False) % 6.62/6.81 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.62/6.81 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.62/6.81 (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) % 6.62/6.81 Clause #21 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1) → big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.62/6.81 (Eq (big_f a_2 (skS.0 2 a a_1 a_2 a_3 a_4) (skS.0 2 a a_1 a_2 a_3 a_4)) False) % 6.62/6.81 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) % 6.62/6.81 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False) % 6.62/6.81 (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)) % 6.62/6.81 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.62/6.81 Or (Eq (big_f a (skS.0 2 a_1 a_2 a a_3 a_4) (skS.0 2 a_1 a_2 a a_3 a_4)) False) % 6.62/6.81 (Or (Eq (big_f (skS.0 0 a_1) (skS.0 1 a_1 a_2) (skS.0 1 a_1 a_2)) False) % 6.62/6.81 (Eq (big_f (skS.0 0 a_1) (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True)) % 6.62/6.81 Clause #24 (by clausification #[18]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_f a a_1 (skS.0 2 a_2 a_3 a a_1 a_4)) True % 6.62/6.81 Clause #25 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), % 6.62/6.81 Eq % 6.62/6.81 (And (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) % 6.62/6.81 (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)))) % 6.62/6.81 False % 6.62/6.81 Clause #26 (by superposition #[24, 16]): ∀ (a a_1 : Iota), % 6.62/6.81 Or (Eq True False) % 6.62/6.81 (Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False) % 6.62/6.81 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True)) % 6.62/6.81 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) False) % 6.62/6.81 (Eq (Iff (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1))) False) % 6.62/6.81 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) False) % 6.62/6.81 (Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False) % 6.62/6.81 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False)) % 6.62/6.81 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 1 a a_1) (skS.0 1 a a_1) a_2) False) % 6.62/6.81 (Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.62/6.81 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True)) % 6.62/6.81 Clause #30 (by superposition #[28, 24]): ∀ (a a_1 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False) % 6.62/6.81 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False) (Eq False True)) % 6.62/6.81 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False) % 6.62/6.81 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False) % 6.62/6.81 Clause #32 (by clausification #[26]): ∀ (a a_1 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) False) % 6.62/6.81 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 6.62/6.81 Clause #33 (by superposition #[29, 24]): ∀ (a a_1 : Iota), % 6.62/6.81 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.62/6.81 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True) (Eq False True)) % 6.62/6.81 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.66/6.86 (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 6.66/6.86 Clause #35 (by superposition #[34, 22]): ∀ (a a_1 a_2 a_3 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.66/6.86 (Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) % 6.66/6.86 (Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True))) % 6.66/6.86 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 a_3 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.66/6.86 (Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)) % 6.66/6.86 Clause #37 (by eliminate duplicate literals #[36]): ∀ (a a_1 a_2 a_3 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) % 6.66/6.86 Clause #38 (by superposition #[37, 31]): ∀ (a a_1 a_2 a_3 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) % 6.66/6.86 (Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False)) % 6.66/6.86 Clause #39 (by superposition #[37, 32]): ∀ (a a_1 a_2 a_3 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) % 6.66/6.86 (Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True)) % 6.66/6.86 Clause #41 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False) % 6.66/6.86 Clause #44 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 6.66/6.86 Clause #46 (by superposition #[44, 41]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Or (Eq (big_f (skS.0 1 a a_1) a_4 a_5) True) (Eq True False)) % 6.66/6.86 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq (big_f (skS.0 1 a a_1) a_4 a_5) True) % 6.66/6.86 Clause #49 (by equality factoring #[47]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne True True) (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) % 6.66/6.86 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Or (Eq True False) (Eq True False)) % 6.66/6.86 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_f (skS.0 1 a a_1) a_2 a_3) True) (Eq True False) % 6.66/6.86 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_f (skS.0 1 a a_1) a_2 a_3) True % 6.66/6.86 Clause #54 (by superposition #[53, 23]): ∀ (a a_1 : Iota), % 6.66/6.86 Or (Eq True False) % 6.66/6.86 (Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False) % 6.66/6.86 (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True)) % 6.66/6.86 Clause #57 (by clausification #[54]): ∀ (a a_1 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False) % 6.66/6.86 (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.66/6.86 Clause #58 (by superposition #[57, 34]): ∀ (a a_1 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.66/6.86 (Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)) % 6.66/6.86 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), % 6.66/6.86 Or (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True) % 6.66/6.86 Clause #60 (by eliminate duplicate literals #[59]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 0 a) (skS.0 1 a a_1)) True % 6.66/6.86 Clause #61 (by backward demodulation #[60, 31]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False) % 6.66/6.86 Clause #62 (by backward demodulation #[60, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True) % 6.66/6.86 Clause #65 (by clausification #[62]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) True % 6.66/6.86 Clause #68 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 0 a) (skS.0 1 a a_1) (skS.0 1 a a_1)) False % 6.66/6.86 Clause #69 (by superposition #[68, 65]): Eq False True % 6.66/6.86 Clause #70 (by clausification #[69]): False % 6.66/6.86 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------