%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN058+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 08:07:04 PM UTC 2025 % Result : Theorem 3.59s 3.79s % Output : Proof 3.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.13 % Problem : SYN058+1 : TPTP v9.2.0. Released v2.0.0. % 0.13/0.14 % Command : duper %s % 0.13/0.36 % Computer : n027.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Thu Oct 2 15:24:23 EDT 2025 % 0.13/0.36 % CPUTime : % 3.59/3.79 SZS status Theorem for theBenchmark.p % 3.59/3.79 SZS output start Proof for theBenchmark.p % 3.59/3.79 Clause #0 (by assumption #[]): Eq (∀ (X : Iota), big_p X → ∀ (Z : Iota), big_q Z) True % 3.59/3.79 Clause #1 (by assumption #[]): Eq ((∀ (X : Iota), Or (big_q X) (big_r X)) → Exists fun X1 => And (big_q X1) (big_s X1)) True % 3.59/3.79 Clause #2 (by assumption #[]): Eq ((Exists fun X => big_s X) → ∀ (X1 : Iota), big_f X1 → big_g X1) True % 3.59/3.79 Clause #3 (by assumption #[]): Eq (Not (∀ (X : Iota), And (big_p X) (big_f X) → big_g X)) True % 3.59/3.79 Clause #4 (by clausification #[3]): Eq (∀ (X : Iota), And (big_p X) (big_f X) → big_g X) False % 3.59/3.79 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (And (big_p (skS.0 0 a)) (big_f (skS.0 0 a)) → big_g (skS.0 0 a))) True % 3.59/3.79 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (And (big_p (skS.0 0 a)) (big_f (skS.0 0 a)) → big_g (skS.0 0 a)) False % 3.59/3.79 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (And (big_p (skS.0 0 a)) (big_f (skS.0 0 a))) True % 3.59/3.79 Clause #8 (by clausification #[6]): ∀ (a : Iota), Eq (big_g (skS.0 0 a)) False % 3.59/3.79 Clause #9 (by clausification #[7]): ∀ (a : Iota), Eq (big_f (skS.0 0 a)) True % 3.59/3.79 Clause #10 (by clausification #[7]): ∀ (a : Iota), Eq (big_p (skS.0 0 a)) True % 3.59/3.79 Clause #11 (by betaEtaReduce #[2]): Eq (Exists big_s → ∀ (X1 : Iota), big_f X1 → big_g X1) True % 3.59/3.79 Clause #12 (by clausification #[11]): Or (Eq (Exists big_s) False) (Eq (∀ (X1 : Iota), big_f X1 → big_g X1) True) % 3.59/3.79 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (∀ (X1 : Iota), big_f X1 → big_g X1) True) (Eq (big_s a) False) % 3.59/3.79 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (big_s a) False) (Eq (big_f a_1 → big_g a_1) True) % 3.59/3.79 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (big_s a) False) (Or (Eq (big_f a_1) False) (Eq (big_g a_1) True)) % 3.59/3.79 Clause #16 (by clausification #[0]): ∀ (a : Iota), Eq (big_p a → ∀ (Z : Iota), big_q Z) True % 3.59/3.79 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (big_p a) False) (Eq (∀ (Z : Iota), big_q Z) True) % 3.59/3.79 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (big_p a) False) (Eq (big_q a_1) True) % 3.59/3.79 Clause #19 (by superposition #[10, 18]): ∀ (a : Iota), Or (Eq (big_q a) True) (Eq False True) % 3.59/3.79 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (big_q a) True % 3.59/3.79 Clause #21 (by clausification #[1]): Or (Eq (∀ (X : Iota), Or (big_q X) (big_r X)) False) (Eq (Exists fun X1 => And (big_q X1) (big_s X1)) True) % 3.59/3.79 Clause #22 (by clausification #[21]): ∀ (a : Iota), % 3.59/3.79 Or (Eq (Exists fun X1 => And (big_q X1) (big_s X1)) True) (Eq (Not (Or (big_q (skS.0 1 a)) (big_r (skS.0 1 a)))) True) % 3.59/3.79 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 3.59/3.79 Or (Eq (Not (Or (big_q (skS.0 1 a)) (big_r (skS.0 1 a)))) True) % 3.59/3.79 (Eq (And (big_q (skS.0 2 a_1)) (big_s (skS.0 2 a_1))) True) % 3.59/3.79 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), % 3.59/3.79 Or (Eq (And (big_q (skS.0 2 a)) (big_s (skS.0 2 a))) True) (Eq (Or (big_q (skS.0 1 a_1)) (big_r (skS.0 1 a_1))) False) % 3.59/3.79 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (Or (big_q (skS.0 1 a)) (big_r (skS.0 1 a))) False) (Eq (big_s (skS.0 2 a_1)) True) % 3.59/3.79 Clause #28 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (big_s (skS.0 2 a)) True) (Eq (big_q (skS.0 1 a_1)) False) % 3.59/3.79 Clause #29 (by superposition #[28, 20]): ∀ (a : Iota), Or (Eq (big_s (skS.0 2 a)) True) (Eq False True) % 3.59/3.79 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (big_s (skS.0 2 a)) True % 3.59/3.79 Clause #31 (by superposition #[30, 15]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (big_f a) False) (Eq (big_g a) True)) % 3.59/3.79 Clause #32 (by clausification #[31]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (big_g a) True) % 3.59/3.79 Clause #33 (by superposition #[32, 9]): ∀ (a : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Eq False True) % 3.59/3.79 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (big_g (skS.0 0 a)) True % 3.59/3.79 Clause #35 (by superposition #[34, 8]): Eq True False % 3.59/3.79 Clause #38 (by clausification #[35]): False % 3.59/3.79 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------