%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN050+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 08:07:03 PM UTC 2025 % Result : Theorem 3.52s 3.67s % Output : Proof 3.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN050+1 : TPTP v9.2.0. Released v2.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n012.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 15:23:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.52/3.67 SZS status Theorem for theBenchmark.p % 3.52/3.67 SZS output start Proof for theBenchmark.p % 3.52/3.67 Clause #0 (by assumption #[]): Eq % 3.52/3.67 (Not % 3.52/3.67 ((∀ (X Y : Iota), Exists fun Z => ∀ (W : Iota), And (big_p X) (big_q Y) → And (big_r Z) (big_s W)) → % 3.52/3.67 Exists fun X1 => Exists fun Y1 => And (big_p X1) (big_q Y1) → Exists fun Z1 => big_r Z1)) % 3.52/3.67 True % 3.52/3.67 Clause #1 (by betaEtaReduce #[0]): Eq % 3.52/3.67 (Not % 3.52/3.67 ((∀ (X Y : Iota), Exists fun Z => ∀ (W : Iota), And (big_p X) (big_q Y) → And (big_r Z) (big_s W)) → % 3.52/3.67 Exists fun X1 => Exists fun Y1 => And (big_p X1) (big_q Y1) → Exists big_r)) % 3.52/3.67 True % 3.52/3.67 Clause #2 (by clausification #[1]): Eq % 3.52/3.67 ((∀ (X Y : Iota), Exists fun Z => ∀ (W : Iota), And (big_p X) (big_q Y) → And (big_r Z) (big_s W)) → % 3.52/3.67 Exists fun X1 => Exists fun Y1 => And (big_p X1) (big_q Y1) → Exists big_r) % 3.52/3.67 False % 3.52/3.67 Clause #3 (by clausification #[2]): Eq (∀ (X Y : Iota), Exists fun Z => ∀ (W : Iota), And (big_p X) (big_q Y) → And (big_r Z) (big_s W)) True % 3.52/3.67 Clause #4 (by clausification #[2]): Eq (Exists fun X1 => Exists fun Y1 => And (big_p X1) (big_q Y1) → Exists big_r) False % 3.52/3.67 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Y : Iota), Exists fun Z => ∀ (W : Iota), And (big_p a) (big_q Y) → And (big_r Z) (big_s W)) True % 3.52/3.67 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (Exists fun Z => ∀ (W : Iota), And (big_p a) (big_q a_1) → And (big_r Z) (big_s W)) True % 3.52/3.67 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Eq (∀ (W : Iota), And (big_p a) (big_q a_1) → And (big_r (skS.0 0 a a_1 a_2)) (big_s W)) True % 3.52/3.67 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (big_p a) (big_q a_1) → And (big_r (skS.0 0 a a_1 a_2)) (big_s a_3)) True % 3.52/3.67 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 3.52/3.67 Or (Eq (And (big_p a) (big_q a_1)) False) (Eq (And (big_r (skS.0 0 a a_1 a_2)) (big_s a_3)) True) % 3.52/3.67 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota), % 3.52/3.67 Or (Eq (And (big_r (skS.0 0 a a_1 a_2)) (big_s a_3)) True) (Or (Eq (big_p a) False) (Eq (big_q a_1) False)) % 3.52/3.67 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a) False) (Or (Eq (big_q a_1) False) (Eq (big_r (skS.0 0 a a_1 a_2)) True)) % 3.52/3.67 Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (Exists fun Y1 => And (big_p a) (big_q Y1) → Exists big_r) False % 3.52/3.67 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (And (big_p a) (big_q a_1) → Exists big_r) False % 3.52/3.67 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (And (big_p a) (big_q a_1)) True % 3.52/3.67 Clause #16 (by clausification #[14]): Eq (Exists big_r) False % 3.52/3.67 Clause #17 (by clausification #[15]): ∀ (a : Iota), Eq (big_q a) True % 3.52/3.67 Clause #18 (by clausification #[15]): ∀ (a : Iota), Eq (big_p a) True % 3.52/3.67 Clause #20 (by clausification #[16]): ∀ (a : Iota), Eq (big_r a) False % 3.52/3.67 Clause #23 (by forward demodulation #[12, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (big_q a) False) (Eq (big_r (skS.0 0 a_1 a a_2)) True)) % 3.52/3.67 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_q a) False) (Eq (big_r (skS.0 0 a_1 a a_2)) True) % 3.52/3.67 Clause #25 (by forward demodulation #[24, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_r (skS.0 0 a a_1 a_2)) True) % 3.52/3.67 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Eq (big_r (skS.0 0 a a_1 a_2)) True % 3.52/3.67 Clause #27 (by superposition #[26, 20]): Eq True False % 3.52/3.67 Clause #28 (by clausification #[27]): False % 3.52/3.67 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------