%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN362+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 08:07:30 PM UTC 2025 % Result : Theorem 3.55s 3.72s % Output : Proof 3.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN362+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n025.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 15:04:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.55/3.72 SZS status Theorem for theBenchmark.p % 3.55/3.72 SZS output start Proof for theBenchmark.p % 3.55/3.72 Clause #0 (by assumption #[]): Eq % 3.55/3.72 (Not % 3.55/3.72 (And (∀ (Y : Iota), Exists fun W => big_r Y W) (Exists fun Z => ∀ (X : Iota), big_p X → Not (big_r Z X)) → % 3.55/3.72 Exists fun X => Not (big_p X))) % 3.55/3.72 True % 3.55/3.72 Clause #1 (by betaEtaReduce #[0]): Eq % 3.55/3.72 (Not % 3.55/3.72 (And (∀ (Y : Iota), Exists (big_r Y)) (Exists fun Z => ∀ (X : Iota), big_p X → Not (big_r Z X)) → % 3.55/3.72 Exists fun X => Not (big_p X))) % 3.55/3.72 True % 3.55/3.72 Clause #2 (by clausification #[1]): Eq % 3.55/3.72 (And (∀ (Y : Iota), Exists (big_r Y)) (Exists fun Z => ∀ (X : Iota), big_p X → Not (big_r Z X)) → % 3.55/3.72 Exists fun X => Not (big_p X)) % 3.55/3.72 False % 3.55/3.72 Clause #3 (by clausification #[2]): Eq (And (∀ (Y : Iota), Exists (big_r Y)) (Exists fun Z => ∀ (X : Iota), big_p X → Not (big_r Z X))) True % 3.55/3.72 Clause #4 (by clausification #[2]): Eq (Exists fun X => Not (big_p X)) False % 3.55/3.72 Clause #5 (by clausification #[3]): Eq (Exists fun Z => ∀ (X : Iota), big_p X → Not (big_r Z X)) True % 3.55/3.72 Clause #6 (by clausification #[3]): Eq (∀ (Y : Iota), Exists (big_r Y)) True % 3.55/3.72 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (X : Iota), big_p X → Not (big_r (skS.0 0 a) X)) True % 3.55/3.72 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (big_p a → Not (big_r (skS.0 0 a_1) a)) True % 3.55/3.72 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (big_p a) False) (Eq (Not (big_r (skS.0 0 a_1) a)) True) % 3.55/3.72 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (big_p a) False) (Eq (big_r (skS.0 0 a_1) a) False) % 3.55/3.72 Clause #11 (by clausification #[6]): ∀ (a : Iota), Eq (Exists (big_r a)) True % 3.55/3.72 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (big_r a (skS.0 1 a a_1)) True % 3.55/3.72 Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (Not (big_p a)) False % 3.55/3.72 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (big_p a) True % 3.55/3.72 Clause #15 (by backward demodulation #[14, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_r (skS.0 0 a) a_1) False) % 3.55/3.72 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (big_r (skS.0 0 a) a_1) False % 3.55/3.72 Clause #17 (by superposition #[16, 12]): Eq False True % 3.55/3.72 Clause #18 (by clausification #[17]): False % 3.55/3.72 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------