%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN364+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 3.75s 3.93s % Output : Proof 3.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN364+1 : TPTP v9.2.0. Released v2.0.0. % 0.11/0.13 % Command : duper %s % 0.12/0.33 % Computer : n022.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 15:35:53 EDT 2025 % 0.12/0.34 % CPUTime : % 3.75/3.93 SZS status Theorem for theBenchmark.p % 3.75/3.93 SZS output start Proof for theBenchmark.p % 3.75/3.93 Clause #0 (by assumption #[]): Eq % 3.75/3.93 (Not % 3.75/3.93 (And % 3.75/3.93 (And (∀ (X : Iota), (Exists fun Y => big_p X Y) → ∀ (Z : Iota), big_p Z Z) % 3.75/3.93 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V))))) % 3.75/3.93 (∀ (W : Iota), big_q W → Not (big_m (g W))) → % 3.75/3.93 ∀ (U : Iota), Exists fun V => And (big_p (g U) V) (big_p U U))) % 3.75/3.93 True % 3.75/3.93 Clause #1 (by betaEtaReduce #[0]): Eq % 3.75/3.93 (Not % 3.75/3.93 (And % 3.75/3.93 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z) % 3.75/3.93 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V))))) % 3.75/3.93 (∀ (W : Iota), big_q W → Not (big_m (g W))) → % 3.75/3.93 ∀ (U : Iota), Exists fun V => And (big_p (g U) V) (big_p U U))) % 3.75/3.93 True % 3.75/3.93 Clause #2 (by clausification #[1]): Eq % 3.75/3.93 (And % 3.75/3.93 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z) % 3.75/3.93 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V))))) % 3.75/3.93 (∀ (W : Iota), big_q W → Not (big_m (g W))) → % 3.75/3.93 ∀ (U : Iota), Exists fun V => And (big_p (g U) V) (big_p U U)) % 3.75/3.93 False % 3.75/3.93 Clause #3 (by clausification #[2]): Eq % 3.75/3.93 (And % 3.75/3.93 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z) % 3.75/3.93 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V))))) % 3.75/3.93 (∀ (W : Iota), big_q W → Not (big_m (g W)))) % 3.75/3.93 True % 3.75/3.93 Clause #4 (by clausification #[2]): Eq (∀ (U : Iota), Exists fun V => And (big_p (g U) V) (big_p U U)) False % 3.75/3.93 Clause #5 (by clausification #[3]): Eq (∀ (W : Iota), big_q W → Not (big_m (g W))) True % 3.75/3.93 Clause #6 (by clausification #[3]): Eq % 3.75/3.93 (And (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z) % 3.75/3.93 (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V))))) % 3.75/3.93 True % 3.75/3.93 Clause #7 (by clausification #[5]): ∀ (a : Iota), Eq (big_q a → Not (big_m (g a))) True % 3.75/3.93 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (big_q a) False) (Eq (Not (big_m (g a))) True) % 3.75/3.93 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (big_q a) False) (Eq (big_m (g a)) False) % 3.75/3.93 Clause #10 (by clausification #[4]): ∀ (a : Iota), Eq (Not (Exists fun V => And (big_p (g (skS.0 0 a)) V) (big_p (skS.0 0 a) (skS.0 0 a)))) True % 3.75/3.93 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (Exists fun V => And (big_p (g (skS.0 0 a)) V) (big_p (skS.0 0 a) (skS.0 0 a))) False % 3.75/3.93 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (And (big_p (g (skS.0 0 a)) a_1) (big_p (skS.0 0 a) (skS.0 0 a))) False % 3.75/3.93 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_p (g (skS.0 0 a)) a_1) False) (Eq (big_p (skS.0 0 a) (skS.0 0 a)) False) % 3.75/3.93 Clause #14 (by clausification #[6]): Eq (∀ (U : Iota), Exists fun V => Or (big_p U V) (And (big_m U) (big_q (f U V)))) True % 3.75/3.93 Clause #15 (by clausification #[6]): Eq (∀ (X : Iota), Exists (big_p X) → ∀ (Z : Iota), big_p Z Z) True % 3.75/3.93 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (Exists fun V => Or (big_p a V) (And (big_m a) (big_q (f a V)))) True % 3.75/3.93 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Or (big_p a (skS.0 1 a a_1)) (And (big_m a) (big_q (f a (skS.0 1 a a_1))))) True % 3.75/3.93 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (big_p a (skS.0 1 a a_1)) True) (Eq (And (big_m a) (big_q (f a (skS.0 1 a a_1)))) True) % 3.75/3.93 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_p a (skS.0 1 a a_1)) True) (Eq (big_q (f a (skS.0 1 a a_1))) True) % 3.75/3.93 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_p a (skS.0 1 a a_1)) True) (Eq (big_m a) True) % 3.75/3.93 Clause #21 (by superposition #[19, 9]): ∀ (a a_1 : Iota), % 3.75/3.93 Or (Eq (big_p a (skS.0 1 a a_1)) True) (Or (Eq True False) (Eq (big_m (g (f a (skS.0 1 a a_1)))) False)) % 3.75/3.93 Clause #22 (by clausification #[15]): ∀ (a : Iota), Eq (Exists (big_p a) → ∀ (Z : Iota), big_p Z Z) True % 3.75/3.93 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (Exists (big_p a)) False) (Eq (∀ (Z : Iota), big_p Z Z) True) % 3.75/3.93 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (∀ (Z : Iota), big_p Z Z) True) (Eq (big_p a a_1) False) % 3.75/3.94 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a_1) False) (Eq (big_p a_2 a_2) True) % 3.75/3.94 Clause #27 (by superposition #[20, 25]): ∀ (a a_1 : Iota), Or (Eq (big_p a a) True) (Or (Eq False True) (Eq (big_m a_1) True)) % 3.75/3.94 Clause #28 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (big_p a (skS.0 1 a a_1)) True) (Eq (big_m (g (f a (skS.0 1 a a_1)))) False) % 3.75/3.94 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (big_p a a) True) (Eq (big_m a_1) True) % 3.75/3.94 Clause #32 (by superposition #[29, 28]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a) True) (Or (Eq (big_p a_1 (skS.0 1 a_1 a_2)) True) (Eq True False)) % 3.75/3.94 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_p a a) True) (Eq (big_p a_1 (skS.0 1 a_1 a_2)) True) % 3.75/3.94 Clause #38 (by superposition #[34, 25]): ∀ (a a_1 : Iota), Or (Eq (big_p a a) True) (Or (Eq True False) (Eq (big_p a_1 a_1) True)) % 3.75/3.94 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (big_p a a) True) (Eq (big_p a_1 a_1) True) % 3.75/3.94 Clause #40 (by equality factoring #[39]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p a a) True) % 3.75/3.94 Clause #41 (by clausification #[40]): ∀ (a : Iota), Or (Eq (big_p a a) True) (Or (Eq True False) (Eq True False)) % 3.75/3.94 Clause #43 (by clausification #[41]): ∀ (a : Iota), Or (Eq (big_p a a) True) (Eq True False) % 3.75/3.94 Clause #44 (by clausification #[43]): ∀ (a : Iota), Eq (big_p a a) True % 3.75/3.94 Clause #45 (by superposition #[44, 13]): ∀ (a : Iota), Or (Eq True False) (Eq (big_p (skS.0 0 a) (skS.0 0 a)) False) % 3.75/3.94 Clause #50 (by clausification #[45]): ∀ (a : Iota), Eq (big_p (skS.0 0 a) (skS.0 0 a)) False % 3.75/3.94 Clause #51 (by superposition #[50, 44]): Eq False True % 3.75/3.94 Clause #52 (by clausification #[51]): False % 3.75/3.94 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------