%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO021^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:08:26 PM UTC 2025 % Result : Theorem 4.16s 4.35s % Output : Proof 4.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SYO021^1 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.12 % Command : duper %s % 0.11/0.33 % Computer : n013.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Fri Oct 3 14:20:53 EDT 2025 % 0.11/0.33 % CPUTime : % 4.16/4.35 SZS status Theorem for theBenchmark.p % 4.16/4.35 SZS output start Proof for theBenchmark.p % 4.16/4.35 Clause #0 (by assumption #[]): Eq (Not (∀ (X Y : Prop), Eq (And X Y) (Not (Or (Not X) (Not Y))))) True % 4.16/4.35 Clause #1 (by clausification #[0]): Eq (∀ (X Y : Prop), Eq (And X Y) (Not (Or (Not X) (Not Y)))) False % 4.16/4.35 Clause #2 (by clausification #[1]): ∀ (a : Prop), Eq (Not (∀ (Y : Prop), Eq (And (skS.0 0 a) Y) (Not (Or (Not (skS.0 0 a)) (Not Y))))) True % 4.16/4.35 Clause #3 (by clausification #[2]): ∀ (a : Prop), Eq (∀ (Y : Prop), Eq (And (skS.0 0 a) Y) (Not (Or (Not (skS.0 0 a)) (Not Y)))) False % 4.16/4.35 Clause #4 (by clausification #[3]): ∀ (a a_1 : Prop), % 4.16/4.35 Eq (Not (Eq (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 % 4.16/4.35 Clause #5 (by clausification #[4]): ∀ (a a_1 : Prop), Eq (Eq (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 % 4.16/4.35 Clause #6 (by clausification #[5]): ∀ (a a_1 : Prop), Ne (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)))) % 4.16/4.35 Clause #7 (by clausification #[6]): ∀ (a a_1 : Prop), % 4.16/4.35 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) % 4.16/4.35 Clause #8 (by clausification #[6]): ∀ (a a_1 : Prop), % 4.16/4.35 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) % 4.16/4.35 Clause #9 (by clausification #[7]): ∀ (a a_1 : Prop), % 4.16/4.35 Or (Eq (Not (Or (Not (skS.0 0 a)) (Not (skS.0 1 a a_1)))) False) % 4.16/4.35 (Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) False)) % 4.16/4.35 Clause #10 (by clausification #[9]): ∀ (a a_1 : Prop), % 4.16/4.35 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)) % 4.16/4.35 Clause #11 (by clausification #[10]): ∀ (a a_1 : Prop), % 4.16/4.35 Or (Eq (skS.0 0 a) False) % 4.16/4.35 (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))) % 4.16/4.35 Clause #12 (by clausification #[11]): ∀ (a a_1 : Prop), % 4.16/4.35 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))) % 4.16/4.35 Clause #13 (by clausification #[12]): ∀ (a a_1 : Prop), % 4.16/4.35 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))) % 4.16/4.35 Clause #14 (by eliminate duplicate literals #[13]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) False) % 4.16/4.35 Clause #16 (by identity boolHoist #[14]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq (skS.0 0 False) False) (Eq a True)) % 4.16/4.35 Clause #23 (by identity boolHoist #[16]): ∀ (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))) % 4.16/4.35 Clause #30 (by identity boolHoist #[23]): ∀ (a a_1 : Prop), % 4.16/4.35 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)))) % 4.16/4.35 Clause #32 (by clausification #[8]): ∀ (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) % 4.16/4.35 Clause #33 (by clausification #[8]): ∀ (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) % 4.16/4.35 Clause #34 (by clausification #[32]): ∀ (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) % 4.16/4.35 Clause #35 (by clausification #[34]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Eq (Not (skS.0 1 a a_1)) False) % 4.16/4.35 Clause #37 (by clausification #[35]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Eq (skS.0 1 a a_1) True) % 4.16/4.35 Clause #38 (by eliminate duplicate literals #[37]): ∀ (a a_1 : Prop), Eq (skS.0 1 a a_1) True % 4.16/4.35 Clause #40 (by identity boolHoist #[38]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a False) True) (Eq a_1 True) % 4.16/4.35 Clause #46 (by identity boolHoist #[40]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (skS.0 1 False False) True) (Eq a_1 True)) % 4.16/4.35 Clause #59 (by equality factoring #[46]): ∀ (a : Prop), Or (Eq (skS.0 1 False False) True) (Or (Ne True True) (Eq a True)) % 4.16/4.35 Clause #60 (by clausification #[59]): ∀ (a : Prop), Or (Eq (skS.0 1 False False) True) (Or (Eq a True) (Or (Eq True False) (Eq True False))) % 4.16/4.37 Clause #62 (by clausification #[60]): ∀ (a : Prop), Or (Eq (skS.0 1 False False) True) (Or (Eq a True) (Eq True False)) % 4.16/4.37 Clause #63 (by clausification #[62]): ∀ (a : Prop), Or (Eq (skS.0 1 False False) True) (Eq a True) % 4.16/4.37 Clause #64 (by equality factoring #[63]): Or (Ne True True) (Eq (skS.0 1 False False) True) % 4.16/4.37 Clause #66 (by clausification #[64]): Or (Eq (skS.0 1 False False) True) (Or (Eq True False) (Eq True False)) % 4.16/4.37 Clause #68 (by clausification #[66]): Or (Eq (skS.0 1 False False) True) (Eq True False) % 4.16/4.37 Clause #69 (by clausification #[68]): Eq (skS.0 1 False False) True % 4.16/4.37 Clause #78 (by eliminate duplicate literals #[30]): ∀ (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))) % 4.16/4.37 Clause #88 (by clausification #[33]): ∀ (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) % 4.16/4.37 Clause #90 (by clausification #[88]): ∀ (a : Prop), Or (Eq (skS.0 0 a) True) (Eq (Not (skS.0 0 a)) False) % 4.16/4.37 Clause #99 (by clausification #[90]): ∀ (a : Prop), Or (Eq (skS.0 0 a) True) (Eq (skS.0 0 a) True) % 4.16/4.37 Clause #100 (by eliminate duplicate literals #[99]): ∀ (a : Prop), Eq (skS.0 0 a) True % 4.16/4.37 Clause #102 (by identity boolHoist #[100]): ∀ (a : Prop), Or (Eq (skS.0 0 False) True) (Eq a True) % 4.16/4.37 Clause #109 (by equality factoring #[102]): Or (Ne True True) (Eq (skS.0 0 False) True) % 4.16/4.37 Clause #111 (by clausification #[109]): Or (Eq (skS.0 0 False) True) (Or (Eq True False) (Eq True False)) % 4.16/4.37 Clause #113 (by clausification #[111]): Or (Eq (skS.0 0 False) True) (Eq True False) % 4.16/4.37 Clause #114 (by clausification #[113]): Eq (skS.0 0 False) True % 4.16/4.37 Clause #116 (by backward demodulation #[114, 78]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq a True) (Or (Eq a_1 True) (Eq (skS.0 1 False False) False))) % 4.16/4.37 Clause #125 (by clausification #[116]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq a_1 True) (Eq (skS.0 1 False False) False)) % 4.16/4.37 Clause #126 (by superposition #[125, 69]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq a_1 True) (Eq False True)) % 4.16/4.37 Clause #127 (by clausification #[126]): ∀ (a a_1 : Prop), Or (Eq a True) (Eq a_1 True) % 4.16/4.37 Clause #132 (by falseElim #[127]): ∀ (a : Prop), Eq a True % 4.16/4.37 Clause #133 (by falseElim #[132]): False % 4.16/4.37 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------