%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:36:58 AM UTC 2026 % Result : Theorem 4.05s 4.30s % Output : Proof 4.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0. % 0.00/0.05 % Command : duper %s % 0.10/0.36 % Computer : n010.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 16:14:09 UTC 2026 % 0.10/0.37 % CPUTime : % 4.05/4.30 SZS status Theorem for theBenchmark.p % 4.05/4.30 SZS output start Proof for theBenchmark.p % 4.05/4.30 Clause #0 (by assumption #[]): Eq (∀ (X Y : Iota), Or (Or (Not (is_a_theorem (implies X Y))) (Not (is_a_theorem X))) (is_a_theorem Y)) True % 4.05/4.30 Clause #1 (by assumption #[]): Eq % 4.05/4.30 (∀ (A B C D E : Iota), % 4.05/4.30 is_a_theorem % 4.05/4.30 (implies (implies A B) % 4.05/4.30 (implies (implies (implies C (implies D E)) (implies B (implies (not D) (not A)))) (implies A D)))) % 4.05/4.30 True % 4.05/4.30 Clause #2 (by assumption #[]): Eq (Not (∀ (A B C : Iota), is_a_theorem (implies (implies A B) (implies (implies B C) (implies A C))))) True % 4.05/4.30 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (Y : Iota), Or (Or (Not (is_a_theorem (implies a Y))) (Not (is_a_theorem a))) (is_a_theorem Y)) True % 4.05/4.30 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), Eq (Or (Or (Not (is_a_theorem (implies a a_1))) (Not (is_a_theorem a))) (is_a_theorem a_1)) True % 4.05/4.30 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 4.05/4.30 Or (Eq (Or (Not (is_a_theorem (implies a a_1))) (Not (is_a_theorem a))) True) (Eq (is_a_theorem a_1) True) % 4.05/4.30 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), % 4.05/4.30 Or (Eq (is_a_theorem a) True) (Or (Eq (Not (is_a_theorem (implies a_1 a))) True) (Eq (Not (is_a_theorem a_1)) True)) % 4.05/4.30 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 4.05/4.30 Or (Eq (is_a_theorem a) True) (Or (Eq (Not (is_a_theorem a_1)) True) (Eq (is_a_theorem (implies a_1 a)) False)) % 4.05/4.30 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.05/4.30 Or (Eq (is_a_theorem a) True) (Or (Eq (is_a_theorem (implies a_1 a)) False) (Eq (is_a_theorem a_1) False)) % 4.05/4.30 Clause #9 (by clausification #[2]): Eq (∀ (A B C : Iota), is_a_theorem (implies (implies A B) (implies (implies B C) (implies A C)))) False % 4.05/4.30 Clause #10 (by clausification #[9]): ∀ (a : Iota), % 4.05/4.30 Eq % 4.05/4.30 (Not % 4.05/4.30 (∀ (B C : Iota), is_a_theorem (implies (implies (skS.0 0 a) B) (implies (implies B C) (implies (skS.0 0 a) C))))) % 4.05/4.30 True % 4.05/4.30 Clause #11 (by clausification #[10]): ∀ (a : Iota), % 4.05/4.30 Eq (∀ (B C : Iota), is_a_theorem (implies (implies (skS.0 0 a) B) (implies (implies B C) (implies (skS.0 0 a) C)))) % 4.05/4.30 False % 4.05/4.30 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 4.05/4.30 Eq % 4.05/4.30 (Not % 4.05/4.30 (∀ (C : Iota), % 4.05/4.30 is_a_theorem % 4.05/4.30 (implies (implies (skS.0 0 a) (skS.0 1 a a_1)) % 4.05/4.30 (implies (implies (skS.0 1 a a_1) C) (implies (skS.0 0 a) C))))) % 4.05/4.30 True % 4.05/4.30 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 4.05/4.30 Eq % 4.05/4.30 (∀ (C : Iota), % 4.05/4.30 is_a_theorem % 4.05/4.30 (implies (implies (skS.0 0 a) (skS.0 1 a a_1)) (implies (implies (skS.0 1 a a_1) C) (implies (skS.0 0 a) C)))) % 4.05/4.30 False % 4.05/4.30 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 4.05/4.30 Eq % 4.05/4.30 (Not % 4.05/4.30 (is_a_theorem % 4.05/4.30 (implies (implies (skS.0 0 a) (skS.0 1 a a_1)) % 4.05/4.30 (implies (implies (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (implies (skS.0 0 a) (skS.0 2 a a_1 a_2)))))) % 4.05/4.30 True % 4.05/4.30 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 4.05/4.30 Eq % 4.05/4.30 (is_a_theorem % 4.05/4.30 (implies (implies (skS.0 0 a) (skS.0 1 a a_1)) % 4.05/4.30 (implies (implies (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) (implies (skS.0 0 a) (skS.0 2 a a_1 a_2))))) % 4.05/4.30 False % 4.05/4.30 Clause #16 (by clausification #[1]): ∀ (a : Iota), % 4.05/4.30 Eq % 4.05/4.30 (∀ (B C D E : Iota), % 4.05/4.30 is_a_theorem % 4.05/4.30 (implies (implies a B) % 4.05/4.30 (implies (implies (implies C (implies D E)) (implies B (implies (not D) (not a)))) (implies a D)))) % 4.05/4.30 True % 4.05/4.30 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 4.05/4.30 Eq % 4.05/4.30 (∀ (C D E : Iota), % 4.05/4.30 is_a_theorem % 4.05/4.30 (implies (implies a a_1) % 4.05/4.30 (implies (implies (implies C (implies D E)) (implies a_1 (implies (not D) (not a)))) (implies a D)))) % 4.05/4.30 True % 4.05/4.30 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 4.05/4.30 Eq % 4.05/4.30 (∀ (D E : Iota), % 4.05/4.30 is_a_theorem % 4.05/4.30 (implies (implies a a_1) % 4.05/4.30 (implies (implies (implies a_2 (implies D E)) (implies a_1 (implies (not D) (not a)))) (implies a D)))) % 4.05/4.30 True % 4.05/4.30 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 : Iota), % 4.05/4.30 Eq % 4.05/4.30 (∀ (E : Iota), % 4.05/4.30 is_a_theorem % 4.05/4.30 (implies (implies a a_1) % 4.05/4.30 (implies (implies (implies a_2 (implies a_3 E)) (implies a_1 (implies (not a_3) (not a)))) (implies a a_3)))) % 4.05/4.32 True % 4.05/4.32 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.05/4.32 Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies (implies a a_1) % 4.05/4.32 (implies (implies (implies a_2 (implies a_3 a_4)) (implies a_1 (implies (not a_3) (not a)))) (implies a a_3)))) % 4.05/4.32 True % 4.05/4.32 Clause #21 (by superposition #[20, 8]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.05/4.32 Or % 4.05/4.32 (Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies (implies (implies a (implies a_1 a_2)) (implies a_3 (implies (not a_1) (not a_4)))) (implies a_4 a_1))) % 4.05/4.32 True) % 4.05/4.32 (Or (Eq True False) (Eq (is_a_theorem (implies a_4 a_3)) False)) % 4.05/4.32 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 4.05/4.32 Or % 4.05/4.32 (Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies (implies (implies a (implies a_1 a_2)) (implies a_3 (implies (not a_1) (not a_4)))) (implies a_4 a_1))) % 4.05/4.32 True) % 4.05/4.32 (Eq (is_a_theorem (implies a_4 a_3)) False) % 4.05/4.32 Clause #23 (by superposition #[22, 20]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.05/4.32 Or % 4.05/4.32 (Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies % 4.05/4.32 (implies (implies a (implies a_1 a_2)) % 4.05/4.32 (implies % 4.05/4.32 (implies (implies (implies a_3 (implies a_4 a_5)) (implies a_6 (implies (not a_4) (not a_7)))) % 4.05/4.32 (implies a_7 a_4)) % 4.05/4.32 (implies (not a_1) (not (implies a_7 a_6))))) % 4.05/4.32 (implies (implies a_7 a_6) a_1))) % 4.05/4.32 True) % 4.05/4.32 (Eq False True) % 4.05/4.32 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.05/4.32 Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies % 4.05/4.32 (implies (implies a (implies a_1 a_2)) % 4.05/4.32 (implies % 4.05/4.32 (implies (implies (implies a_3 (implies a_4 a_5)) (implies a_6 (implies (not a_4) (not a_7)))) % 4.05/4.32 (implies a_7 a_4)) % 4.05/4.32 (implies (not a_1) (not (implies a_7 a_6))))) % 4.05/4.32 (implies (implies a_7 a_6) a_1))) % 4.05/4.32 True % 4.05/4.32 Clause #25 (by superposition #[24, 8]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.05/4.32 Or (Eq (is_a_theorem (implies (implies a a_1) a_2)) True) % 4.05/4.32 (Or (Eq True False) % 4.05/4.32 (Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies (implies a_3 (implies a_2 a_4)) % 4.05/4.32 (implies % 4.05/4.32 (implies (implies (implies a_5 (implies a_6 a_7)) (implies a_1 (implies (not a_6) (not a)))) % 4.05/4.32 (implies a a_6)) % 4.05/4.32 (implies (not a_2) (not (implies a a_1)))))) % 4.05/4.32 False)) % 4.05/4.32 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.05/4.32 Or (Eq (is_a_theorem (implies (implies a a_1) a_2)) True) % 4.05/4.32 (Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies (implies a_3 (implies a_2 a_4)) % 4.05/4.32 (implies % 4.05/4.32 (implies (implies (implies a_5 (implies a_6 a_7)) (implies a_1 (implies (not a_6) (not a)))) % 4.05/4.32 (implies a a_6)) % 4.05/4.32 (implies (not a_2) (not (implies a a_1)))))) % 4.05/4.32 False) % 4.05/4.32 Clause #28 (by superposition #[27, 24]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.05/4.32 Or % 4.05/4.32 (Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies (implies a a_1) % 4.05/4.32 (implies % 4.05/4.32 (implies (implies a_2 (implies a_3 a_4)) % 4.05/4.32 (implies (implies a a_5) % 4.05/4.32 (implies (not a_3) % 4.05/4.32 (not (implies (implies a_6 (implies a_5 a_7)) (implies a_1 (implies (not a_5) (not a)))))))) % 4.05/4.32 (implies (implies (implies a_6 (implies a_5 a_7)) (implies a_1 (implies (not a_5) (not a)))) a_3)))) % 4.05/4.32 True) % 4.05/4.32 (Eq False True) % 4.05/4.32 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.05/4.32 Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies (implies a a_1) % 4.05/4.32 (implies % 4.05/4.32 (implies (implies a_2 (implies a_3 a_4)) % 4.05/4.32 (implies (implies a a_5) % 4.05/4.32 (implies (not a_3) % 4.05/4.32 (not (implies (implies a_6 (implies a_5 a_7)) (implies a_1 (implies (not a_5) (not a)))))))) % 4.05/4.32 (implies (implies (implies a_6 (implies a_5 a_7)) (implies a_1 (implies (not a_5) (not a)))) a_3)))) % 4.05/4.32 True % 4.05/4.32 Clause #30 (by superposition #[29, 8]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.05/4.32 Or % 4.05/4.32 (Eq % 4.05/4.32 (is_a_theorem % 4.05/4.32 (implies % 4.05/4.32 (implies (implies a (implies a_1 a_2)) % 4.05/4.32 (implies (implies a_3 a_4) % 4.05/4.32 (implies (not a_1) % 4.05/4.32 (not (implies (implies a_5 (implies a_4 a_6)) (implies a_7 (implies (not a_4) (not a_3)))))))) % 4.05/4.34 (implies (implies (implies a_5 (implies a_4 a_6)) (implies a_7 (implies (not a_4) (not a_3)))) a_1))) % 4.05/4.34 True) % 4.05/4.34 (Or (Eq True False) (Eq (is_a_theorem (implies a_3 a_7)) False)) % 4.05/4.34 Clause #31 (by superposition #[29, 22]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota), % 4.05/4.34 Or % 4.05/4.34 (Eq % 4.05/4.34 (is_a_theorem % 4.05/4.34 (implies % 4.05/4.34 (implies (implies a (implies a_1 a_2)) % 4.05/4.34 (implies % 4.05/4.34 (implies % 4.05/4.34 (implies (implies a_3 (implies a_4 a_5)) % 4.05/4.34 (implies (implies a_6 a_7) % 4.05/4.34 (implies (not a_4) % 4.05/4.34 (not (implies (implies a_8 (implies a_7 a_9)) (implies a_10 (implies (not a_7) (not a_6)))))))) % 4.05/4.34 (implies (implies (implies a_8 (implies a_7 a_9)) (implies a_10 (implies (not a_7) (not a_6)))) a_4)) % 4.05/4.34 (implies (not a_1) (not (implies a_6 a_10))))) % 4.05/4.34 (implies (implies a_6 a_10) a_1))) % 4.05/4.34 True) % 4.05/4.34 (Eq True False) % 4.05/4.34 Clause #32 (by clausification #[30]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 4.05/4.34 Or % 4.05/4.34 (Eq % 4.05/4.34 (is_a_theorem % 4.05/4.34 (implies % 4.05/4.34 (implies (implies a (implies a_1 a_2)) % 4.05/4.34 (implies (implies a_3 a_4) % 4.05/4.34 (implies (not a_1) % 4.05/4.34 (not (implies (implies a_5 (implies a_4 a_6)) (implies a_7 (implies (not a_4) (not a_3)))))))) % 4.05/4.34 (implies (implies (implies a_5 (implies a_4 a_6)) (implies a_7 (implies (not a_4) (not a_3)))) a_1))) % 4.05/4.34 True) % 4.05/4.34 (Eq (is_a_theorem (implies a_3 a_7)) False) % 4.05/4.34 Clause #33 (by superposition #[32, 20]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota), % 4.05/4.34 Or % 4.05/4.34 (Eq % 4.05/4.34 (is_a_theorem % 4.05/4.34 (implies % 4.05/4.34 (implies (implies a (implies a_1 a_2)) % 4.05/4.34 (implies (implies (implies a_3 a_4) a_5) % 4.05/4.34 (implies (not a_1) % 4.05/4.34 (not % 4.05/4.34 (implies (implies a_6 (implies a_5 a_7)) % 4.05/4.34 (implies % 4.05/4.34 (implies (implies (implies a_8 (implies a_9 a_10)) (implies a_4 (implies (not a_9) (not a_3)))) % 4.05/4.34 (implies a_3 a_9)) % 4.05/4.34 (implies (not a_5) (not (implies a_3 a_4))))))))) % 4.05/4.34 (implies % 4.05/4.34 (implies (implies a_6 (implies a_5 a_7)) % 4.05/4.34 (implies % 4.05/4.34 (implies (implies (implies a_8 (implies a_9 a_10)) (implies a_4 (implies (not a_9) (not a_3)))) % 4.05/4.34 (implies a_3 a_9)) % 4.05/4.34 (implies (not a_5) (not (implies a_3 a_4))))) % 4.05/4.34 a_1))) % 4.05/4.34 True) % 4.05/4.34 (Eq False True) % 4.05/4.34 Clause #36 (by clausification #[31]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota), % 4.05/4.34 Eq % 4.05/4.34 (is_a_theorem % 4.05/4.34 (implies % 4.05/4.34 (implies (implies a (implies a_1 a_2)) % 4.05/4.34 (implies % 4.05/4.34 (implies % 4.05/4.34 (implies (implies a_3 (implies a_4 a_5)) % 4.05/4.34 (implies (implies a_6 a_7) % 4.05/4.34 (implies (not a_4) % 4.05/4.34 (not (implies (implies a_8 (implies a_7 a_9)) (implies a_10 (implies (not a_7) (not a_6)))))))) % 4.05/4.34 (implies (implies (implies a_8 (implies a_7 a_9)) (implies a_10 (implies (not a_7) (not a_6)))) a_4)) % 4.05/4.34 (implies (not a_1) (not (implies a_6 a_10))))) % 4.05/4.34 (implies (implies a_6 a_10) a_1))) % 4.05/4.34 True % 4.05/4.34 Clause #37 (by superposition #[36, 8]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota), % 4.05/4.34 Or (Eq (is_a_theorem (implies (implies a a_1) a_2)) True) % 4.05/4.34 (Or (Eq True False) % 4.05/4.34 (Eq % 4.05/4.34 (is_a_theorem % 4.05/4.34 (implies (implies a_3 (implies a_2 a_4)) % 4.05/4.34 (implies % 4.05/4.34 (implies % 4.05/4.34 (implies (implies a_5 (implies a_6 a_7)) % 4.05/4.34 (implies (implies a a_8) % 4.05/4.34 (implies (not a_6) % 4.05/4.34 (not (implies (implies a_9 (implies a_8 a_10)) (implies a_1 (implies (not a_8) (not a)))))))) % 4.05/4.34 (implies (implies (implies a_9 (implies a_8 a_10)) (implies a_1 (implies (not a_8) (not a)))) a_6)) % 4.05/4.34 (implies (not a_2) (not (implies a a_1)))))) % 4.05/4.34 False)) % 4.05/4.34 Clause #41 (by clausification #[37]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota), % 4.05/4.35 Or (Eq (is_a_theorem (implies (implies a a_1) a_2)) True) % 4.05/4.35 (Eq % 4.05/4.35 (is_a_theorem % 4.05/4.35 (implies (implies a_3 (implies a_2 a_4)) % 4.05/4.35 (implies % 4.05/4.35 (implies % 4.05/4.35 (implies (implies a_5 (implies a_6 a_7)) % 4.05/4.35 (implies (implies a a_8) % 4.05/4.35 (implies (not a_6) % 4.05/4.35 (not (implies (implies a_9 (implies a_8 a_10)) (implies a_1 (implies (not a_8) (not a)))))))) % 4.05/4.35 (implies (implies (implies a_9 (implies a_8 a_10)) (implies a_1 (implies (not a_8) (not a)))) a_6)) % 4.05/4.35 (implies (not a_2) (not (implies a a_1)))))) % 4.05/4.35 False) % 4.05/4.35 Clause #44 (by clausification #[33]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 a_10 : Iota), % 4.05/4.35 Eq % 4.05/4.35 (is_a_theorem % 4.05/4.35 (implies % 4.05/4.35 (implies (implies a (implies a_1 a_2)) % 4.05/4.35 (implies (implies (implies a_3 a_4) a_5) % 4.05/4.35 (implies (not a_1) % 4.05/4.35 (not % 4.05/4.35 (implies (implies a_6 (implies a_5 a_7)) % 4.05/4.35 (implies % 4.05/4.35 (implies (implies (implies a_8 (implies a_9 a_10)) (implies a_4 (implies (not a_9) (not a_3)))) % 4.05/4.35 (implies a_3 a_9)) % 4.05/4.35 (implies (not a_5) (not (implies a_3 a_4))))))))) % 4.05/4.35 (implies % 4.05/4.35 (implies (implies a_6 (implies a_5 a_7)) % 4.05/4.35 (implies % 4.05/4.35 (implies (implies (implies a_8 (implies a_9 a_10)) (implies a_4 (implies (not a_9) (not a_3)))) % 4.05/4.35 (implies a_3 a_9)) % 4.05/4.35 (implies (not a_5) (not (implies a_3 a_4))))) % 4.05/4.35 a_1))) % 4.05/4.35 True % 4.05/4.35 Clause #49 (by superposition #[44, 41]): ∀ (a a_1 a_2 : Iota), % 4.05/4.35 Or (Eq (is_a_theorem (implies (implies a a_1) (implies (implies a_1 a_2) (implies a a_2)))) True) (Eq True False) % 4.05/4.35 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), Eq (is_a_theorem (implies (implies a a_1) (implies (implies a_1 a_2) (implies a a_2)))) True % 4.05/4.35 Clause #52 (by superposition #[50, 15]): Eq True False % 4.05/4.35 Clause #55 (by clausification #[52]): False % 4.05/4.35 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------