%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN358+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:07:29 PM UTC 2025 % Result : Theorem 3.68s 3.86s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN358+1 : TPTP v9.2.0. Released v2.0.0. % 0.13/0.13 % Command : duper %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 15:16:23 EDT 2025 % 0.20/0.35 % CPUTime : % 3.68/3.86 SZS status Theorem for theBenchmark.p % 3.68/3.86 SZS output start Proof for theBenchmark.p % 3.68/3.86 Clause #0 (by assumption #[]): Eq (Not (Iff (Exists fun X => And p (big_q X)) (And p (Exists fun X => big_q X)))) True % 3.68/3.86 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Exists fun X => And p (big_q X)) (And p (Exists big_q)))) True % 3.68/3.86 Clause #2 (by clausification #[1]): Eq (Iff (Exists fun X => And p (big_q X)) (And p (Exists big_q))) False % 3.68/3.86 Clause #3 (by clausification #[2]): Or (Eq (Exists fun X => And p (big_q X)) False) (Eq (And p (Exists big_q)) False) % 3.68/3.86 Clause #4 (by clausification #[2]): Or (Eq (Exists fun X => And p (big_q X)) True) (Eq (And p (Exists big_q)) True) % 3.68/3.86 Clause #5 (by clausification #[3]): ∀ (a : Iota), Or (Eq (And p (Exists big_q)) False) (Eq (And p (big_q a)) False) % 3.68/3.86 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (And p (big_q a)) False) (Or (Eq p False) (Eq (Exists big_q) False)) % 3.68/3.86 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq p False) (Or (Eq (Exists big_q) False) (Or (Eq p False) (Eq (big_q a) False))) % 3.68/3.86 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq p False) (Or (Eq (big_q a) False) (Eq (big_q a_1) False))) % 3.68/3.86 Clause #9 (by eliminate duplicate literals #[8]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq (big_q a) False) (Eq (big_q a_1) False)) % 3.68/3.86 Clause #10 (by clausification #[4]): ∀ (a : Iota), Or (Eq (And p (Exists big_q)) True) (Eq (And p (big_q (skS.0 0 a))) True) % 3.68/3.86 Clause #11 (by clausification #[10]): ∀ (a : Iota), Or (Eq (And p (big_q (skS.0 0 a))) True) (Eq (Exists big_q) True) % 3.68/3.86 Clause #12 (by clausification #[10]): ∀ (a : Iota), Or (Eq (And p (big_q (skS.0 0 a))) True) (Eq p True) % 3.68/3.86 Clause #13 (by clausification #[11]): ∀ (a : Iota), Or (Eq (Exists big_q) True) (Eq (big_q (skS.0 0 a)) True) % 3.68/3.86 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Eq (big_q (skS.0 1 a_1)) True) % 3.68/3.86 Clause #18 (by clausification #[12]): Or (Eq p True) (Eq p True) % 3.68/3.86 Clause #19 (by eliminate duplicate literals #[18]): Eq p True % 3.68/3.86 Clause #20 (by backward demodulation #[19, 9]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_q a) False) (Eq (big_q a_1) False)) % 3.68/3.86 Clause #23 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (big_q a) False) (Eq (big_q a_1) False) % 3.68/3.86 Clause #25 (by superposition #[23, 15]): ∀ (a a_1 : Iota), Or (Eq (big_q a) False) (Or (Eq (big_q (skS.0 0 a_1)) True) (Eq False True)) % 3.68/3.86 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (big_q a) False) (Eq (big_q (skS.0 0 a_1)) True) % 3.68/3.86 Clause #28 (by superposition #[26, 15]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq (big_q (skS.0 0 a_1)) True) (Eq False True)) % 3.68/3.86 Clause #32 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Eq (big_q (skS.0 0 a_1)) True) % 3.68/3.86 Clause #36 (by equality factoring #[32]): ∀ (a : Iota), Or (Ne True True) (Eq (big_q (skS.0 0 a)) True) % 3.68/3.86 Clause #37 (by clausification #[36]): ∀ (a : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 3.68/3.86 Clause #39 (by clausification #[37]): ∀ (a : Iota), Or (Eq (big_q (skS.0 0 a)) True) (Eq True False) % 3.68/3.86 Clause #40 (by clausification #[39]): ∀ (a : Iota), Eq (big_q (skS.0 0 a)) True % 3.68/3.86 Clause #41 (by superposition #[40, 23]): ∀ (a : Iota), Or (Eq True False) (Eq (big_q a) False) % 3.68/3.86 Clause #43 (by clausification #[41]): ∀ (a : Iota), Eq (big_q a) False % 3.68/3.86 Clause #44 (by superposition #[43, 40]): Eq False True % 3.68/3.86 Clause #45 (by clausification #[44]): False % 3.68/3.86 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------