%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO390^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 08:08:59 PM UTC 2025 % Result : Theorem 3.60s 3.79s % Output : Proof 3.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SYO390^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.15 % Command : duper %s % 0.13/0.36 % Computer : n009.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Fri Oct 3 14:27:53 EDT 2025 % 0.13/0.36 % CPUTime : % 3.60/3.79 SZS status Theorem for theBenchmark.p % 3.60/3.79 SZS output start Proof for theBenchmark.p % 3.60/3.79 Clause #0 (by assumption #[]): Eq (Not (∀ (Xp Xq : Prop), Iff Xp Xq → Eq Xp Xq)) True % 3.60/3.79 Clause #1 (by clausification #[0]): Eq (∀ (Xp Xq : Prop), Iff Xp Xq → Eq Xp Xq) False % 3.60/3.79 Clause #2 (by clausification #[1]): ∀ (a : Prop), Eq (Not (∀ (Xq : Prop), Iff (skS.0 0 a) Xq → Eq (skS.0 0 a) Xq)) True % 3.60/3.79 Clause #3 (by clausification #[2]): ∀ (a : Prop), Eq (∀ (Xq : Prop), Iff (skS.0 0 a) Xq → Eq (skS.0 0 a) Xq) False % 3.60/3.79 Clause #4 (by clausification #[3]): ∀ (a a_1 : Prop), Eq (Not (Iff (skS.0 0 a) (skS.0 1 a a_1) → Eq (skS.0 0 a) (skS.0 1 a a_1))) True % 3.60/3.79 Clause #5 (by clausification #[4]): ∀ (a a_1 : Prop), Eq (Iff (skS.0 0 a) (skS.0 1 a a_1) → Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 3.60/3.79 Clause #6 (by clausification #[5]): ∀ (a a_1 : Prop), Eq (Iff (skS.0 0 a) (skS.0 1 a a_1)) True % 3.60/3.79 Clause #7 (by clausification #[5]): ∀ (a a_1 : Prop), Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 3.60/3.79 Clause #8 (by clausification #[6]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) True) (Eq (skS.0 1 a a_1) False) % 3.60/3.79 Clause #9 (by clausification #[6]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) True) % 3.60/3.79 Clause #10 (by identity loobHoist #[8]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq (skS.0 0 True) True) (Eq a False)) % 3.60/3.79 Clause #12 (by identity loobHoist #[10]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq (skS.0 1 a True) False) (Eq a_1 False))) % 3.60/3.79 Clause #14 (by identity loobHoist #[12]): ∀ (a a_1 : Prop), % 3.60/3.79 Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 True True) False) (Eq a False)))) % 3.60/3.79 Clause #16 (by eliminate duplicate literals #[14]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False))) % 3.60/3.79 Clause #17 (by falseElim #[16]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Eq (skS.0 1 True True) False)) % 3.60/3.79 Clause #18 (by identity loobHoist #[9]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq (skS.0 0 True) False) (Eq a False)) % 3.60/3.79 Clause #20 (by identity loobHoist #[18]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq (skS.0 1 a True) True) (Eq a_1 False))) % 3.60/3.79 Clause #22 (by identity loobHoist #[20]): ∀ (a a_1 : Prop), % 3.60/3.79 Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 True True) True) (Eq a False)))) % 3.60/3.79 Clause #24 (by eliminate duplicate literals #[22]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) True))) % 3.60/3.79 Clause #25 (by clausification #[7]): ∀ (a a_1 : Prop), Ne (skS.0 0 a) (skS.0 1 a a_1) % 3.60/3.79 Clause #26 (by clausification #[25]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) False) % 3.60/3.79 Clause #27 (by clausification #[25]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) True) (Eq (skS.0 1 a a_1) True) % 3.60/3.79 Clause #28 (by identity loobHoist #[26]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq (skS.0 0 True) False) (Eq a False)) % 3.60/3.79 Clause #30 (by identity loobHoist #[28]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq (skS.0 1 a True) False) (Eq a_1 False))) % 3.60/3.79 Clause #32 (by identity loobHoist #[30]): ∀ (a a_1 : Prop), % 3.60/3.79 Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 True True) False) (Eq a False)))) % 3.60/3.79 Clause #34 (by eliminate duplicate literals #[32]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False))) % 3.60/3.79 Clause #35 (by identity loobHoist #[27]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq (skS.0 0 True) True) (Eq a False)) % 3.60/3.79 Clause #37 (by identity loobHoist #[35]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq (skS.0 1 a True) True) (Eq a_1 False))) % 3.60/3.79 Clause #39 (by identity loobHoist #[37]): ∀ (a a_1 : Prop), % 3.60/3.79 Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 True True) True) (Eq a False)))) % 3.60/3.79 Clause #41 (by eliminate duplicate literals #[39]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) True))) % 3.60/3.80 Clause #42 (by falseElim #[41]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Eq (skS.0 1 True True) True)) % 3.60/3.80 Clause #43 (by falseElim #[17]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) False) % 3.60/3.80 Clause #48 (by falseElim #[42]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) True) % 3.60/3.80 Clause #49 (by superposition #[48, 43]): Or (Eq (skS.0 0 True) True) (Or (Eq (skS.0 0 True) True) (Eq True False)) % 3.60/3.80 Clause #50 (by clausification #[49]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 0 True) True) % 3.60/3.80 Clause #51 (by eliminate duplicate literals #[50]): Eq (skS.0 0 True) True % 3.60/3.80 Clause #52 (by backward demodulation #[51, 24]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) True))) % 3.60/3.80 Clause #53 (by backward demodulation #[51, 34]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False))) % 3.60/3.80 Clause #57 (by clausification #[53]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False)) % 3.60/3.80 Clause #59 (by falseElim #[57]): ∀ (a : Prop), Or (Eq a False) (Eq (skS.0 1 True True) False) % 3.60/3.80 Clause #61 (by falseElim #[59]): Eq (skS.0 1 True True) False % 3.60/3.80 Clause #62 (by clausification #[52]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) True)) % 3.60/3.80 Clause #64 (by falseElim #[62]): ∀ (a : Prop), Or (Eq a False) (Eq (skS.0 1 True True) True) % 3.60/3.80 Clause #66 (by falseElim #[64]): Eq (skS.0 1 True True) True % 3.60/3.80 Clause #67 (by superposition #[66, 61]): Eq True False % 3.60/3.80 Clause #68 (by clausification #[67]): False % 3.60/3.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------