%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO382^5 : TPTP v9.2.0. Released v4.0.0. % 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 08:08:58 PM UTC 2025 % Result : Theorem 3.36s 3.57s % Output : Proof 3.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYO382^5 : TPTP v9.2.0. Released v4.0.0. % 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 : Fri Oct 3 13:43:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.36/3.57 SZS status Theorem for theBenchmark.p % 3.36/3.57 SZS output start Proof for theBenchmark.p % 3.36/3.57 Clause #0 (by assumption #[]): Eq % 3.36/3.57 (Not % 3.36/3.57 ((And (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) % 3.36/3.57 (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy)) → % 3.36/3.57 Exists fun Xu => Not (cS Xu)) → % 3.36/3.57 And (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) % 3.36/3.57 (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy)) → % 3.36/3.57 Exists fun Xu => Not (cS Xu))) % 3.36/3.57 True % 3.36/3.57 Clause #1 (by clausification #[0]): Eq % 3.36/3.57 ((And (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) % 3.36/3.57 (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy)) → % 3.36/3.57 Exists fun Xu => Not (cS Xu)) → % 3.36/3.57 And (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) % 3.36/3.57 (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy)) → % 3.36/3.57 Exists fun Xu => Not (cS Xu)) % 3.36/3.57 False % 3.36/3.57 Clause #3 (by clausification #[1]): Eq % 3.36/3.57 (And (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) % 3.36/3.57 (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy)) → % 3.36/3.57 Exists fun Xu => Not (cS Xu)) % 3.36/3.57 False % 3.36/3.57 Clause #22 (by clausification #[3]): Eq % 3.36/3.57 (And (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) % 3.36/3.57 (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy))) % 3.36/3.57 True % 3.36/3.57 Clause #23 (by clausification #[3]): Eq (Exists fun Xu => Not (cS Xu)) False % 3.36/3.57 Clause #24 (by clausification #[22]): Eq (∀ (Xx Xy : Iota), cP Xx Xy → Not (cQ Xx Xy)) True % 3.36/3.57 Clause #25 (by clausification #[22]): Eq (And (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx)) True % 3.36/3.57 Clause #26 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Xy : Iota), cP a Xy → Not (cQ a Xy)) True % 3.36/3.57 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (cP a a_1 → Not (cQ a a_1)) True % 3.36/3.57 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (cP a a_1) False) (Eq (Not (cQ a a_1)) True) % 3.36/3.57 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (cP a a_1) False) (Eq (cQ a a_1) False) % 3.36/3.57 Clause #30 (by clausification #[23]): ∀ (a : Iota), Eq (Not (cS a)) False % 3.36/3.57 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (cS a) True % 3.36/3.57 Clause #32 (by clausification #[25]): Eq (∀ (Xx : Iota), cS Xx → Exists fun Xy => cQ Xy Xx) True % 3.36/3.57 Clause #33 (by clausification #[25]): Eq (Exists fun Xv => ∀ (Xx : Iota), cP Xx Xv) True % 3.36/3.57 Clause #34 (by clausification #[32]): ∀ (a : Iota), Eq (cS a → Exists fun Xy => cQ Xy a) True % 3.36/3.57 Clause #35 (by clausification #[34]): ∀ (a : Iota), Or (Eq (cS a) False) (Eq (Exists fun Xy => cQ Xy a) True) % 3.36/3.57 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (cS a) False) (Eq (cQ (skS.0 5 a a_1) a) True) % 3.36/3.57 Clause #37 (by forward demodulation #[36, 31]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cQ (skS.0 5 a a_1) a) True) % 3.36/3.57 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (cQ (skS.0 5 a a_1) a) True % 3.36/3.57 Clause #39 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (Xx : Iota), cP Xx (skS.0 6 a)) True % 3.36/3.57 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (cP a (skS.0 6 a_1)) True % 3.36/3.57 Clause #41 (by superposition #[40, 29]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (cQ a (skS.0 6 a_1)) False) % 3.36/3.57 Clause #47 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (cQ a (skS.0 6 a_1)) False % 3.36/3.57 Clause #48 (by superposition #[47, 38]): Eq False True % 3.36/3.57 Clause #49 (by clausification #[48]): False % 3.36/3.57 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------