%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN370+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:07:31 PM UTC 2025 % Result : Theorem 5.64s 5.82s % Output : Proof 5.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SYN370+1 : TPTP v9.2.0. Released v2.0.0. % 0.06/0.12 % Command : duper %s % 0.12/0.32 % Computer : n005.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 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 15:23:38 EDT 2025 % 0.12/0.33 % CPUTime : % 5.64/5.82 SZS status Theorem for theBenchmark.p % 5.64/5.82 SZS output start Proof for theBenchmark.p % 5.64/5.82 Clause #0 (by assumption #[]): Eq (Not (Exists fun V => ∀ (Y : Iota), Exists fun Z => Or (big_p a Y (h Y)) (big_p V Y (f Y)) → big_p V Y Z)) True % 5.64/5.82 Clause #1 (by clausification #[0]): Eq (Exists fun V => ∀ (Y : Iota), Exists fun Z => Or (big_p a Y (h Y)) (big_p V Y (f Y)) → big_p V Y Z) False % 5.64/5.82 Clause #2 (by clausification #[1]): ∀ (a_1 : Iota), Eq (∀ (Y : Iota), Exists fun Z => Or (big_p a Y (h Y)) (big_p a_1 Y (f Y)) → big_p a_1 Y Z) False % 5.64/5.82 Clause #3 (by clausification #[2]): ∀ (a_1 a_2 : Iota), % 5.64/5.82 Eq % 5.64/5.82 (Not % 5.64/5.82 (Exists fun Z => % 5.64/5.82 Or (big_p a (skS.0 0 a_1 a_2) (h (skS.0 0 a_1 a_2))) (big_p a_1 (skS.0 0 a_1 a_2) (f (skS.0 0 a_1 a_2))) → % 5.64/5.82 big_p a_1 (skS.0 0 a_1 a_2) Z)) % 5.64/5.82 True % 5.64/5.82 Clause #4 (by clausification #[3]): ∀ (a_1 a_2 : Iota), % 5.64/5.82 Eq % 5.64/5.82 (Exists fun Z => % 5.64/5.82 Or (big_p a (skS.0 0 a_1 a_2) (h (skS.0 0 a_1 a_2))) (big_p a_1 (skS.0 0 a_1 a_2) (f (skS.0 0 a_1 a_2))) → % 5.64/5.82 big_p a_1 (skS.0 0 a_1 a_2) Z) % 5.64/5.82 False % 5.64/5.82 Clause #5 (by clausification #[4]): ∀ (a_1 a_2 a_3 : Iota), % 5.64/5.82 Eq % 5.64/5.82 (Or (big_p a (skS.0 0 a_1 a_2) (h (skS.0 0 a_1 a_2))) (big_p a_1 (skS.0 0 a_1 a_2) (f (skS.0 0 a_1 a_2))) → % 5.64/5.82 big_p a_1 (skS.0 0 a_1 a_2) a_3) % 5.64/5.82 False % 5.64/5.82 Clause #6 (by clausification #[5]): ∀ (a_1 a_2 : Iota), % 5.64/5.82 Eq (Or (big_p a (skS.0 0 a_1 a_2) (h (skS.0 0 a_1 a_2))) (big_p a_1 (skS.0 0 a_1 a_2) (f (skS.0 0 a_1 a_2)))) True % 5.64/5.82 Clause #7 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (big_p a (skS.0 0 a a_1) a_2) False % 5.64/5.82 Clause #8 (by clausification #[6]): ∀ (a_1 a_2 : Iota), % 5.64/5.82 Or (Eq (big_p a (skS.0 0 a_1 a_2) (h (skS.0 0 a_1 a_2))) True) % 5.64/5.82 (Eq (big_p a_1 (skS.0 0 a_1 a_2) (f (skS.0 0 a_1 a_2))) True) % 5.64/5.82 Clause #9 (by superposition #[7, 8]): ∀ (a_1 a_2 : Iota), Or (Eq (big_p a (skS.0 0 a_1 a_2) (h (skS.0 0 a_1 a_2))) True) (Eq True False) % 5.64/5.82 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 : Iota), Eq (big_p a (skS.0 0 a_1 a_2) (h (skS.0 0 a_1 a_2))) True % 5.64/5.82 Clause #12 (by superposition #[10, 7]): Eq True False % 5.64/5.82 Clause #13 (by clausification #[12]): False % 5.64/5.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------