%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO019^1 : TPTP v9.2.0. Released v3.7.0. % 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 08:08:25 PM UTC 2025 % Result : Theorem 4.19s 4.37s % Output : Proof 4.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO019^1 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.14 % 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 : Fri Oct 3 13:32:08 EDT 2025 % 0.13/0.35 % CPUTime : % 4.19/4.37 SZS status Theorem for theBenchmark.p % 4.19/4.37 SZS output start Proof for theBenchmark.p % 4.19/4.37 Clause #0 (by assumption #[]): Eq (Not (∀ (X Y : Prop), Iff (And X Y) (Not (Or (Not X) (Not Y))))) True % 4.19/4.37 Clause #1 (by clausification #[0]): Eq (∀ (X Y : Prop), Iff (And X Y) (Not (Or (Not X) (Not Y)))) False % 4.19/4.37 Clause #2 (by clausification #[1]): ∀ (a : Prop), Eq (Not (∀ (Y : Prop), Iff (And (skS.0 0 a) Y) (Not (Or (Not (skS.0 0 a)) (Not Y))))) True % 4.19/4.37 Clause #3 (by clausification #[2]): ∀ (a : Prop), Eq (∀ (Y : Prop), Iff (And (skS.0 0 a) Y) (Not (Or (Not (skS.0 0 a)) (Not Y)))) False % 4.19/4.37 Clause #4 (by clausification #[3]): ∀ (a a_1 : Prop), % 4.19/4.37 Eq (Not (Iff (And (skS.0 0 a) (skS.0 1 a a_1)) (Not (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1)))))) True % 4.19/4.37 Clause #5 (by clausification #[4]): ∀ (a a_1 : Prop), Eq (Iff (And (skS.0 0 a) (skS.0 1 a a_1)) (Not (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1))))) False % 4.19/4.37 Clause #6 (by clausification #[5]): ∀ (a a_1 : Prop), % 4.19/4.37 Or (Eq (And (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (Not (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1)))) False) % 4.19/4.37 Clause #7 (by clausification #[5]): ∀ (a a_1 : Prop), % 4.19/4.37 Or (Eq (And (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (Not (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1)))) True) % 4.19/4.37 Clause #8 (by clausification #[6]): ∀ (a a_1 : Prop), % 4.19/4.37 Or (Eq (Not (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1)))) False) % 4.19/4.37 (Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) False)) % 4.19/4.37 Clause #9 (by clausification #[8]): ∀ (a a_1 : Prop), % 4.19/4.37 Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a a_1) False) (Eq (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1))) True)) % 4.19/4.37 Clause #10 (by clausification #[9]): ∀ (a a_1 : Prop), % 4.19/4.37 Or (Eq (skS.0 0 a) False) % 4.19/4.37 (Or (Eq (skS.0 1 a a_1) False) (Or (Eq (Not (skS.0 0 a)) True) (Eq (Not (skS.0 1 a a_1)) True))) % 4.19/4.37 Clause #11 (by clausification #[10]): ∀ (a a_1 : Prop), % 4.19/4.37 Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a a_1) False) (Or (Eq (Not (skS.0 1 a a_1)) True) (Eq (skS.0 0 a) False))) % 4.19/4.37 Clause #12 (by clausification #[11]): ∀ (a a_1 : Prop), % 4.19/4.37 Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a a_1) False) (Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) False))) % 4.19/4.37 Clause #13 (by eliminate duplicate literals #[12]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) False) % 4.19/4.37 Clause #15 (by identity boolHoist #[13]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq (skS.0 0 False) False) (Eq a True)) % 4.19/4.37 Clause #22 (by identity boolHoist #[15]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 False) False) (Or (Eq a True) (Or (Eq (skS.0 1 a False) False) (Eq a_1 True))) % 4.19/4.37 Clause #29 (by identity boolHoist #[22]): ∀ (a a_1 : Prop), % 4.19/4.37 Or (Eq (skS.0 0 False) False) (Or (Eq a True) (Or (Eq a_1 True) (Or (Eq (skS.0 1 False False) False) (Eq a True)))) % 4.19/4.37 Clause #31 (by clausification #[7]): ∀ (a a_1 : Prop), Or (Eq (Not (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1)))) True) (Eq (skS.0 1 a a_1) True) % 4.19/4.37 Clause #32 (by clausification #[7]): ∀ (a a_1 : Prop), Or (Eq (Not (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1)))) True) (Eq (skS.0 0 a) True) % 4.19/4.37 Clause #33 (by clausification #[31]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Eq (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1))) False) % 4.19/4.37 Clause #34 (by clausification #[33]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Eq (Not (skS.0 1 a a_1)) False) % 4.19/4.37 Clause #36 (by clausification #[34]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Eq (skS.0 1 a a_1) True) % 4.19/4.37 Clause #37 (by eliminate duplicate literals #[36]): ∀ (a a_1 : Prop), Eq (skS.0 1 a a_1) True % 4.19/4.37 Clause #39 (by identity boolHoist #[37]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a False) True) (Eq a_1 True) % 4.19/4.37 Clause #45 (by identity boolHoist #[39]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (skS.0 1 False False) True) (Eq a_1 True)) % 4.19/4.37 Clause #58 (by equality factoring #[45]): ∀ (a : Prop), Or (Eq (skS.0 1 False False) True) (Or (Ne True True) (Eq a True)) % 4.19/4.37 Clause #59 (by clausification #[58]): ∀ (a : Prop), Or (Eq (skS.0 1 False False) True) (Or (Eq a True) (Or (Eq True False) (Eq True False))) % 4.19/4.37 Clause #61 (by clausification #[59]): ∀ (a : Prop), Or (Eq (skS.0 1 False False) True) (Or (Eq a True) (Eq True False)) % 4.19/4.38 Clause #62 (by clausification #[61]): ∀ (a : Prop), Or (Eq (skS.0 1 False False) True) (Eq a True) % 4.19/4.38 Clause #63 (by equality factoring #[62]): Or (Ne True True) (Eq (skS.0 1 False False) True) % 4.19/4.38 Clause #65 (by clausification #[63]): Or (Eq (skS.0 1 False False) True) (Or (Eq True False) (Eq True False)) % 4.19/4.38 Clause #67 (by clausification #[65]): Or (Eq (skS.0 1 False False) True) (Eq True False) % 4.19/4.38 Clause #68 (by clausification #[67]): Eq (skS.0 1 False False) True % 4.19/4.38 Clause #77 (by eliminate duplicate literals #[29]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 False) False) (Or (Eq a True) (Or (Eq a_1 True) (Eq (skS.0 1 False False) False))) % 4.19/4.38 Clause #87 (by clausification #[32]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) True) (Eq (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1))) False) % 4.19/4.38 Clause #89 (by clausification #[87]): ∀ (a : Prop), Or (Eq (skS.0 0 a) True) (Eq (Not (skS.0 0 a)) False) % 4.19/4.38 Clause #98 (by clausification #[89]): ∀ (a : Prop), Or (Eq (skS.0 0 a) True) (Eq (skS.0 0 a) True) % 4.19/4.38 Clause #99 (by eliminate duplicate literals #[98]): ∀ (a : Prop), Eq (skS.0 0 a) True % 4.19/4.38 Clause #101 (by identity boolHoist #[99]): ∀ (a : Prop), Or (Eq (skS.0 0 False) True) (Eq a True) % 4.19/4.38 Clause #108 (by equality factoring #[101]): Or (Ne True True) (Eq (skS.0 0 False) True) % 4.19/4.38 Clause #110 (by clausification #[108]): Or (Eq (skS.0 0 False) True) (Or (Eq True False) (Eq True False)) % 4.19/4.38 Clause #112 (by clausification #[110]): Or (Eq (skS.0 0 False) True) (Eq True False) % 4.19/4.38 Clause #113 (by clausification #[112]): Eq (skS.0 0 False) True % 4.19/4.38 Clause #115 (by backward demodulation #[113, 77]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq a True) (Or (Eq a_1 True) (Eq (skS.0 1 False False) False))) % 4.19/4.38 Clause #124 (by clausification #[115]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq a_1 True) (Eq (skS.0 1 False False) False)) % 4.19/4.38 Clause #125 (by superposition #[124, 68]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq a_1 True) (Eq False True)) % 4.19/4.38 Clause #126 (by clausification #[125]): ∀ (a a_1 : Prop), Or (Eq a True) (Eq a_1 True) % 4.19/4.38 Clause #131 (by falseElim #[126]): ∀ (a : Prop), Eq a True % 4.19/4.38 Clause #132 (by falseElim #[131]): False % 4.19/4.38 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------