%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO111^5 : TPTP v9.2.0. Released v4.0.0. % 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 08:08:36 PM UTC 2025 % Result : Theorem 3.97s 4.16s % Output : Proof 3.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYO111^5 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.13/0.35 % Computer : n027.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 : Fri Oct 3 14:32:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.97/4.16 SZS status Theorem for theBenchmark.p % 3.97/4.16 SZS output start Proof for theBenchmark.p % 3.97/4.16 Clause #0 (by assumption #[]): Eq % 3.97/4.16 (Not % 3.97/4.16 (Or % 3.97/4.16 (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) % 3.97/4.16 (Not (Or (∀ (Y : Iota), cM Y) (Exists fun S => cN S)))) % 3.97/4.16 (Not (Or (∀ (Z : Iota), Not (cN Z)) (Not (∀ (T : Iota), cG T)))) → % 3.97/4.16 Or % 3.97/4.16 (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) % 3.97/4.16 (Not (∀ (Y : Iota), Or (cM Y) (Exists fun S => cN S)))) % 3.97/4.16 (Not (∀ (Z : Iota), Or (Not (cN Z)) (Not (∀ (T : Iota), cG T)))))) % 3.97/4.16 True % 3.97/4.16 Clause #1 (by betaEtaReduce #[0]): Eq % 3.97/4.16 (Not % 3.97/4.16 (Or (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (Or (∀ (Y : Iota), cM Y) (Exists cN)))) % 3.97/4.16 (Not (Or (∀ (Z : Iota), Not (cN Z)) (Not (∀ (T : Iota), cG T)))) → % 3.97/4.16 Or (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (∀ (Y : Iota), Or (cM Y) (Exists cN)))) % 3.97/4.16 (Not (∀ (Z : Iota), Or (Not (cN Z)) (Not (∀ (T : Iota), cG T)))))) % 3.97/4.16 True % 3.97/4.16 Clause #2 (by clausification #[1]): Eq % 3.97/4.16 (Or (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (Or (∀ (Y : Iota), cM Y) (Exists cN)))) % 3.97/4.16 (Not (Or (∀ (Z : Iota), Not (cN Z)) (Not (∀ (T : Iota), cG T)))) → % 3.97/4.16 Or (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (∀ (Y : Iota), Or (cM Y) (Exists cN)))) % 3.97/4.16 (Not (∀ (Z : Iota), Or (Not (cN Z)) (Not (∀ (T : Iota), cG T))))) % 3.97/4.16 False % 3.97/4.16 Clause #4 (by clausification #[2]): Eq % 3.97/4.16 (Or (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (∀ (Y : Iota), Or (cM Y) (Exists cN)))) % 3.97/4.16 (Not (∀ (Z : Iota), Or (Not (cN Z)) (Not (∀ (T : Iota), cG T))))) % 3.97/4.16 False % 3.97/4.16 Clause #40 (by clausification #[4]): Eq (Not (∀ (Z : Iota), Or (Not (cN Z)) (Not (∀ (T : Iota), cG T)))) False % 3.97/4.16 Clause #41 (by clausification #[4]): Eq (Or (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) (Not (∀ (Y : Iota), Or (cM Y) (Exists cN)))) False % 3.97/4.16 Clause #42 (by clausification #[40]): Eq (∀ (Z : Iota), Or (Not (cN Z)) (Not (∀ (T : Iota), cG T))) True % 3.97/4.16 Clause #43 (by clausification #[42]): ∀ (a : Iota), Eq (Or (Not (cN a)) (Not (∀ (T : Iota), cG T))) True % 3.97/4.16 Clause #44 (by clausification #[43]): ∀ (a : Iota), Or (Eq (Not (cN a)) True) (Eq (Not (∀ (T : Iota), cG T)) True) % 3.97/4.16 Clause #45 (by clausification #[44]): ∀ (a : Iota), Or (Eq (Not (∀ (T : Iota), cG T)) True) (Eq (cN a) False) % 3.97/4.16 Clause #46 (by clausification #[45]): ∀ (a : Iota), Or (Eq (cN a) False) (Eq (∀ (T : Iota), cG T) False) % 3.97/4.16 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (cN a) False) (Eq (Not (cG (skS.0 6 a_1))) True) % 3.97/4.16 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (cN a) False) (Eq (cG (skS.0 6 a_1)) False) % 3.97/4.16 Clause #49 (by clausification #[41]): Eq (Not (∀ (Y : Iota), Or (cM Y) (Exists cN))) False % 3.97/4.16 Clause #50 (by clausification #[41]): Eq (Or (∀ (R : Iota), cM R) (Exists fun X => Not (cG X))) False % 3.97/4.16 Clause #51 (by clausification #[49]): Eq (∀ (Y : Iota), Or (cM Y) (Exists cN)) True % 3.97/4.16 Clause #52 (by clausification #[51]): ∀ (a : Iota), Eq (Or (cM a) (Exists cN)) True % 3.97/4.16 Clause #53 (by clausification #[52]): ∀ (a : Iota), Or (Eq (cM a) True) (Eq (Exists cN) True) % 3.97/4.16 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), Or (Eq (cM a) True) (Eq (cN (skS.0 7 a_1)) True) % 3.97/4.16 Clause #56 (by clausification #[50]): Eq (Exists fun X => Not (cG X)) False % 3.97/4.16 Clause #57 (by clausification #[50]): Eq (∀ (R : Iota), cM R) False % 3.97/4.16 Clause #58 (by clausification #[56]): ∀ (a : Iota), Eq (Not (cG a)) False % 3.97/4.16 Clause #59 (by clausification #[58]): ∀ (a : Iota), Eq (cG a) True % 3.97/4.16 Clause #62 (by clausification #[57]): ∀ (a : Iota), Eq (Not (cM (skS.0 8 a))) True % 3.97/4.16 Clause #63 (by clausification #[62]): ∀ (a : Iota), Eq (cM (skS.0 8 a)) False % 3.97/4.16 Clause #64 (by superposition #[63, 54]): ∀ (a : Iota), Or (Eq False True) (Eq (cN (skS.0 7 a)) True) % 3.97/4.16 Clause #65 (by clausification #[64]): ∀ (a : Iota), Eq (cN (skS.0 7 a)) True % 3.97/4.16 Clause #66 (by superposition #[65, 48]): ∀ (a : Iota), Or (Eq True False) (Eq (cG (skS.0 6 a)) False) % 3.97/4.16 Clause #67 (by clausification #[66]): ∀ (a : Iota), Eq (cG (skS.0 6 a)) False % 3.97/4.16 Clause #68 (by superposition #[67, 59]): Eq False True % 3.97/4.16 Clause #69 (by clausification #[68]): False % 3.97/4.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------