%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN054+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 3.73s 3.90s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SYN054+1 : TPTP v9.2.0. Released v2.0.0. % 0.13/0.15 % Command : duper %s % 0.15/0.36 % Computer : n031.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Thu Oct 2 15:35:23 EDT 2025 % 0.15/0.36 % CPUTime : % 3.73/3.90 SZS status Theorem for theBenchmark.p % 3.73/3.90 SZS output start Proof for theBenchmark.p % 3.73/3.90 Clause #0 (by assumption #[]): Eq (Not (Exists fun X => And (big_s X) (big_q X))) True % 3.73/3.90 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), big_p X → Or (big_q X) (big_r X)) True % 3.73/3.90 Clause #2 (by assumption #[]): Eq (Not (Exists fun X => big_p X) → Exists fun Y => big_q Y) True % 3.73/3.90 Clause #3 (by assumption #[]): Eq (∀ (X : Iota), Or (big_q X) (big_r X) → big_s X) True % 3.73/3.90 Clause #4 (by assumption #[]): Eq (Not (Exists fun X => And (big_p X) (big_r X))) True % 3.73/3.90 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (Or (big_q a) (big_r a) → big_s a) True % 3.73/3.90 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (Or (big_q a) (big_r a)) False) (Eq (big_s a) True) % 3.73/3.90 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq (big_s a) True) (Eq (big_q a) False) % 3.73/3.90 Clause #9 (by betaEtaReduce #[2]): Eq (Not (Exists big_p) → Exists big_q) True % 3.73/3.90 Clause #10 (by clausification #[9]): Or (Eq (Not (Exists big_p)) False) (Eq (Exists big_q) True) % 3.73/3.90 Clause #11 (by clausification #[10]): Or (Eq (Exists big_q) True) (Eq (Exists big_p) True) % 3.73/3.90 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (Exists big_p) True) (Eq (big_q (skS.0 0 a)) True) % 3.73/3.90 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Eq (big_p (skS.0 1 a_1)) True) % 3.73/3.90 Clause #14 (by superposition #[13, 8]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq (big_s (skS.0 0 a_1)) True) (Eq True False)) % 3.73/3.90 Clause #15 (by clausification #[1]): ∀ (a : Iota), Eq (big_p a → Or (big_q a) (big_r a)) True % 3.73/3.90 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (big_p a) False) (Eq (Or (big_q a) (big_r a)) True) % 3.73/3.90 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (big_p a) False) (Or (Eq (big_q a) True) (Eq (big_r a) True)) % 3.73/3.90 Clause #19 (by clausification #[4]): Eq (Exists fun X => And (big_p X) (big_r X)) False % 3.73/3.90 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (And (big_p a) (big_r a)) False % 3.73/3.90 Clause #21 (by clausification #[20]): ∀ (a : Iota), Or (Eq (big_p a) False) (Eq (big_r a) False) % 3.73/3.91 Clause #23 (by clausification #[0]): Eq (Exists fun X => And (big_s X) (big_q X)) False % 3.73/3.91 Clause #24 (by clausification #[23]): ∀ (a : Iota), Eq (And (big_s a) (big_q a)) False % 3.73/3.91 Clause #25 (by clausification #[24]): ∀ (a : Iota), Or (Eq (big_s a) False) (Eq (big_q a) False) % 3.73/3.91 Clause #26 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (big_s (skS.0 0 a_1)) True) % 3.73/3.91 Clause #29 (by superposition #[26, 25]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq True False) (Eq (big_q (skS.0 0 a_1)) False)) % 3.73/3.91 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (big_q (skS.0 0 a_1)) False) % 3.73/3.91 Clause #31 (by superposition #[30, 13]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq False True) (Eq (big_p (skS.0 1 a_1)) True)) % 3.73/3.91 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq (big_p (skS.0 1 a_1)) True) % 3.73/3.91 Clause #35 (by equality factoring #[32]): ∀ (a : Iota), Or (Ne True True) (Eq (big_p (skS.0 1 a)) True) % 3.73/3.91 Clause #36 (by clausification #[35]): ∀ (a : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 3.73/3.91 Clause #38 (by clausification #[36]): ∀ (a : Iota), Or (Eq (big_p (skS.0 1 a)) True) (Eq True False) % 3.73/3.91 Clause #39 (by clausification #[38]): ∀ (a : Iota), Eq (big_p (skS.0 1 a)) True % 3.73/3.91 Clause #40 (by superposition #[39, 17]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (big_q (skS.0 1 a)) True) (Eq (big_r (skS.0 1 a)) True)) % 3.73/3.91 Clause #41 (by superposition #[39, 21]): ∀ (a : Iota), Or (Eq True False) (Eq (big_r (skS.0 1 a)) False) % 3.73/3.91 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (big_r (skS.0 1 a)) False % 3.73/3.91 Clause #47 (by clausification #[40]): ∀ (a : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Eq (big_r (skS.0 1 a)) True) % 3.73/3.91 Clause #48 (by superposition #[47, 42]): ∀ (a : Iota), Or (Eq (big_q (skS.0 1 a)) True) (Eq True False) % 3.73/3.91 Clause #50 (by clausification #[48]): ∀ (a : Iota), Eq (big_q (skS.0 1 a)) True % 3.73/3.91 Clause #52 (by superposition #[50, 8]): ∀ (a : Iota), Or (Eq (big_s (skS.0 1 a)) True) (Eq True False) % 3.73/3.91 Clause #53 (by clausification #[52]): ∀ (a : Iota), Eq (big_s (skS.0 1 a)) True % 3.73/3.91 Clause #54 (by superposition #[53, 25]): ∀ (a : Iota), Or (Eq True False) (Eq (big_q (skS.0 1 a)) False) % 3.73/3.91 Clause #55 (by clausification #[54]): ∀ (a : Iota), Eq (big_q (skS.0 1 a)) False % 3.73/3.91 Clause #56 (by superposition #[55, 50]): Eq False True % 3.73/3.91 Clause #58 (by clausification #[56]): False % 3.73/3.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------