%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO099^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:08:35 PM UTC 2025 % Result : Theorem 3.54s 3.77s % Output : Proof 3.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO099^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n019.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 13:40:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.54/3.77 SZS status Theorem for theBenchmark.p % 3.54/3.77 SZS output start Proof for theBenchmark.p % 3.54/3.77 Clause #0 (by assumption #[]): Eq % 3.54/3.77 (Not % 3.54/3.77 (Or % 3.54/3.77 (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (Or (∀ (Y : Iota), cM Y) (Exists fun S => cN S)))) % 3.54/3.77 (Not (Or (∀ (Z : Iota), Not (cN Z)) (Not (∀ (T : Iota), cG T)))))) % 3.54/3.77 True % 3.54/3.77 Clause #1 (by betaEtaReduce #[0]): Eq % 3.54/3.77 (Not % 3.54/3.77 (Or (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (Or (∀ (Y : Iota), cM Y) (Exists cN)))) % 3.54/3.77 (Not (Or (∀ (Z : Iota), Not (cN Z)) (Not (∀ (T : Iota), cG T)))))) % 3.54/3.77 True % 3.54/3.77 Clause #2 (by clausification #[1]): Eq % 3.54/3.77 (Or (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (Or (∀ (Y : Iota), cM Y) (Exists cN)))) % 3.54/3.77 (Not (Or (∀ (Z : Iota), Not (cN Z)) (Not (∀ (T : Iota), cG T))))) % 3.54/3.77 False % 3.54/3.77 Clause #3 (by clausification #[2]): Eq (Not (Or (∀ (Z : Iota), Not (cN Z)) (Not (∀ (T : Iota), cG T)))) False % 3.54/3.77 Clause #4 (by clausification #[2]): Eq (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (Or (∀ (Y : Iota), cM Y) (Exists cN)))) False % 3.54/3.77 Clause #5 (by clausification #[3]): Eq (Or (∀ (Z : Iota), Not (cN Z)) (Not (∀ (T : Iota), cG T))) True % 3.54/3.77 Clause #6 (by clausification #[5]): Or (Eq (∀ (Z : Iota), Not (cN Z)) True) (Eq (Not (∀ (T : Iota), cG T)) True) % 3.54/3.77 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (Not (∀ (T : Iota), cG T)) True) (Eq (Not (cN a)) True) % 3.54/3.77 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (Not (cN a)) True) (Eq (∀ (T : Iota), cG T) False) % 3.54/3.77 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (∀ (T : Iota), cG T) False) (Eq (cN a) False) % 3.54/3.77 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (cN a) False) (Eq (Not (cG (skS.0 0 a_1))) True) % 3.54/3.77 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (cN a) False) (Eq (cG (skS.0 0 a_1)) False) % 3.54/3.77 Clause #12 (by clausification #[4]): Eq (Not (Or (∀ (Y : Iota), cM Y) (Exists cN))) False % 3.54/3.77 Clause #13 (by clausification #[4]): Eq (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) False % 3.54/3.77 Clause #14 (by clausification #[12]): Eq (Or (∀ (Y : Iota), cM Y) (Exists cN)) True % 3.54/3.77 Clause #15 (by clausification #[14]): Or (Eq (∀ (Y : Iota), cM Y) True) (Eq (Exists cN) True) % 3.54/3.77 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (Exists cN) True) (Eq (cM a) True) % 3.54/3.77 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (cM a) True) (Eq (cN (skS.0 1 a_1)) True) % 3.54/3.77 Clause #18 (by superposition #[17, 11]): ∀ (a a_1 : Iota), Or (Eq (cM a) True) (Or (Eq True False) (Eq (cG (skS.0 0 a_1)) False)) % 3.54/3.77 Clause #19 (by clausification #[13]): Eq (Exists fun X => Not (cG X)) False % 3.54/3.77 Clause #20 (by clausification #[13]): Eq (∀ (R : Iota), cM R) False % 3.54/3.77 Clause #21 (by clausification #[19]): ∀ (a : Iota), Eq (Not (cG a)) False % 3.54/3.77 Clause #22 (by clausification #[21]): ∀ (a : Iota), Eq (cG a) True % 3.54/3.77 Clause #23 (by clausification #[20]): ∀ (a : Iota), Eq (Not (cM (skS.0 2 a))) True % 3.54/3.77 Clause #24 (by clausification #[23]): ∀ (a : Iota), Eq (cM (skS.0 2 a)) False % 3.54/3.77 Clause #28 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (cM a) True) (Eq (cG (skS.0 0 a_1)) False) % 3.54/3.77 Clause #29 (by superposition #[28, 22]): ∀ (a : Iota), Or (Eq (cM a) True) (Eq False True) % 3.54/3.77 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (cM a) True % 3.54/3.77 Clause #31 (by superposition #[30, 24]): Eq True False % 3.54/3.77 Clause #32 (by clausification #[31]): False % 3.54/3.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------