%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO207^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:08:45 PM UTC 2025 % Result : Theorem 4.22s 4.41s % Output : Proof 4.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYO207^5 : TPTP v9.2.0. Released v4.0.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n001.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 14:03:38 EDT 2025 % 0.13/0.35 % CPUTime : % 4.22/4.41 SZS status Theorem for theBenchmark.p % 4.22/4.41 SZS output start Proof for theBenchmark.p % 4.22/4.41 Clause #0 (by assumption #[]): Eq (Not (∀ (Xx Xy : Prop), Eq (Eq Xx Xy) (Eq Xy Xx))) True % 4.22/4.41 Clause #1 (by clausification #[0]): Eq (∀ (Xx Xy : Prop), Eq (Eq Xx Xy) (Eq Xy Xx)) False % 4.22/4.41 Clause #2 (by clausification #[1]): ∀ (a : Prop), Eq (Not (∀ (Xy : Prop), Eq (Eq (skS.0 0 a) Xy) (Eq Xy (skS.0 0 a)))) True % 4.22/4.41 Clause #3 (by clausification #[2]): ∀ (a : Prop), Eq (∀ (Xy : Prop), Eq (Eq (skS.0 0 a) Xy) (Eq Xy (skS.0 0 a))) False % 4.22/4.41 Clause #4 (by clausification #[3]): ∀ (a a_1 : Prop), Eq (Not (Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) (Eq (skS.0 1 a a_1) (skS.0 0 a)))) True % 4.22/4.41 Clause #5 (by clausification #[4]): ∀ (a a_1 : Prop), Eq (Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) (Eq (skS.0 1 a a_1) (skS.0 0 a))) False % 4.22/4.41 Clause #6 (by clausification #[5]): ∀ (a a_1 : Prop), Ne (Eq (skS.0 0 a) (skS.0 1 a a_1)) (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 4.22/4.41 Clause #7 (by clausification #[6]): ∀ (a a_1 : Prop), Or (Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (Eq (skS.0 1 a a_1) (skS.0 0 a)) False) % 4.22/4.41 Clause #8 (by clausification #[6]): ∀ (a a_1 : Prop), Or (Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (Eq (skS.0 1 a a_1) (skS.0 0 a)) True) % 4.22/4.41 Clause #9 (by clausification #[7]): ∀ (a a_1 : Prop), Or (Eq (Eq (skS.0 1 a a_1) (skS.0 0 a)) False) (Ne (skS.0 0 a) (skS.0 1 a a_1)) % 4.22/4.41 Clause #10 (by clausification #[9]): ∀ (a a_1 : Prop), Or (Ne (skS.0 0 a) (skS.0 1 a a_1)) (Ne (skS.0 1 a a_1) (skS.0 0 a)) % 4.22/4.41 Clause #11 (by clausification #[10]): ∀ (a a_1 : Prop), Or (Ne (skS.0 1 a a_1) (skS.0 0 a)) (Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) False)) % 4.22/4.41 Clause #12 (by clausification #[10]): ∀ (a a_1 : Prop), Or (Ne (skS.0 1 a a_1) (skS.0 0 a)) (Or (Eq (skS.0 0 a) True) (Eq (skS.0 1 a a_1) True)) % 4.22/4.41 Clause #13 (by clausification #[11]): ∀ (a a_1 : Prop), % 4.22/4.41 Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a a_1) False) (Or (Eq (skS.0 1 a a_1) False) (Eq (skS.0 0 a) False))) % 4.22/4.41 Clause #15 (by eliminate duplicate literals #[13]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) False) % 4.22/4.41 Clause #16 (by identity loobHoist #[15]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq (skS.0 0 True) False) (Eq a False)) % 4.22/4.41 Clause #18 (by identity loobHoist #[16]): ∀ (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))) % 4.22/4.41 Clause #20 (by identity loobHoist #[18]): ∀ (a a_1 : Prop), % 4.22/4.41 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)))) % 4.22/4.41 Clause #22 (by eliminate duplicate literals #[20]): ∀ (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))) % 4.22/4.41 Clause #33 (by clausification #[8]): ∀ (a a_1 : Prop), Or (Eq (Eq (skS.0 1 a a_1) (skS.0 0 a)) True) (Eq (skS.0 0 a) (skS.0 1 a a_1)) % 4.22/4.41 Clause #34 (by clausification #[33]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) (skS.0 1 a a_1)) (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 4.22/4.41 Clause #35 (by eliminate duplicate literals #[34]): ∀ (a a_1 : Prop), Eq (skS.0 0 a) (skS.0 1 a a_1) % 4.22/4.41 Clause #36 (by identity loobHoist #[35]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) (skS.0 1 a a_1)) (Eq a False) % 4.22/4.41 Clause #38 (by identity loobHoist #[36]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq (skS.0 0 True) (skS.0 1 a True)) (Eq a_1 False)) % 4.22/4.41 Clause #40 (by identity loobHoist #[38]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq a_1 False) (Or (Eq (skS.0 0 True) (skS.0 1 True True)) (Eq a False))) % 4.22/4.41 Clause #42 (by eliminate duplicate literals #[40]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 0 True) (skS.0 1 True True))) % 4.22/4.41 Clause #43 (by falseElim #[42]): ∀ (a : Prop), Or (Eq a False) (Eq (skS.0 0 True) (skS.0 1 True True)) % 4.22/4.41 Clause #44 (by falseElim #[43]): Eq (skS.0 0 True) (skS.0 1 True True) % 4.22/4.41 Clause #49 (by clausification #[12]): ∀ (a a_1 : Prop), % 4.22/4.41 Or (Eq (skS.0 0 a) True) (Or (Eq (skS.0 1 a a_1) True) (Or (Eq (skS.0 1 a a_1) True) (Eq (skS.0 0 a) True))) % 4.22/4.41 Clause #108 (by eliminate duplicate literals #[49]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) True) (Eq (skS.0 1 a a_1) True) % 4.22/4.42 Clause #109 (by identity loobHoist #[108]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq (skS.0 0 True) True) (Eq a False)) % 4.22/4.42 Clause #111 (by identity loobHoist #[109]): ∀ (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))) % 4.22/4.42 Clause #113 (by identity loobHoist #[111]): ∀ (a a_1 : Prop), % 4.22/4.42 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)))) % 4.22/4.42 Clause #115 (by eliminate duplicate literals #[113]): ∀ (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))) % 4.22/4.42 Clause #120 (by falseElim #[115]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Eq (skS.0 1 True True) True)) % 4.22/4.42 Clause #129 (by falseElim #[120]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) True) % 4.22/4.42 Clause #130 (by superposition #[129, 44]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 0 True) True) % 4.22/4.42 Clause #132 (by eliminate duplicate literals #[130]): Eq (skS.0 0 True) True % 4.22/4.42 Clause #133 (by backward demodulation #[132, 22]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False))) % 4.22/4.42 Clause #135 (by backward demodulation #[132, 44]): Eq True (skS.0 1 True True) % 4.22/4.42 Clause #160 (by clausification #[133]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False)) % 4.22/4.42 Clause #165 (by falseElim #[160]): ∀ (a : Prop), Or (Eq a False) (Eq (skS.0 1 True True) False) % 4.22/4.42 Clause #170 (by falseElim #[165]): Eq (skS.0 1 True True) False % 4.22/4.42 Clause #171 (by superposition #[170, 135]): Eq True False % 4.22/4.42 Clause #172 (by clausification #[171]): False % 4.22/4.42 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------