%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO299^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:08:52 PM UTC 2025 % Result : Theorem 5.83s 6.02s % Output : Proof 5.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.10 % Problem : SYO299^5 : TPTP v9.2.0. Released v4.0.0. % 0.02/0.11 % Command : duper %s % 0.10/0.31 % Computer : n020.cluster.edu % 0.10/0.31 % Model : x86_64 x86_64 % 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.31 % Memory : 8042.1875MB % 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.31 % CPULimit : 300 % 0.10/0.31 % WCLimit : 300 % 0.10/0.31 % DateTime : Fri Oct 3 14:00:38 EDT 2025 % 0.10/0.31 % CPUTime : % 5.83/6.02 SZS status Theorem for theBenchmark.p % 5.83/6.02 SZS output start Proof for theBenchmark.p % 5.83/6.02 Clause #0 (by assumption #[]): Eq (Not (∀ (P Q R : Prop), Exists fun S => Iff (Iff P Q) R → Iff P (Iff Q S))) True % 5.83/6.02 Clause #1 (by clausification #[0]): Eq (∀ (P Q R : Prop), Exists fun S => Iff (Iff P Q) R → Iff P (Iff Q S)) False % 5.83/6.02 Clause #2 (by clausification #[1]): ∀ (a : Prop), Eq (Not (∀ (Q R : Prop), Exists fun S => Iff (Iff (skS.0 0 a) Q) R → Iff (skS.0 0 a) (Iff Q S))) True % 5.83/6.02 Clause #3 (by clausification #[2]): ∀ (a : Prop), Eq (∀ (Q R : Prop), Exists fun S => Iff (Iff (skS.0 0 a) Q) R → Iff (skS.0 0 a) (Iff Q S)) False % 5.83/6.02 Clause #4 (by clausification #[3]): ∀ (a a_1 : Prop), % 5.83/6.02 Eq % 5.83/6.02 (Not % 5.83/6.02 (∀ (R : Prop), Exists fun S => Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) R → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) S))) % 5.83/6.02 True % 5.83/6.02 Clause #5 (by clausification #[4]): ∀ (a a_1 : Prop), % 5.83/6.02 Eq (∀ (R : Prop), Exists fun S => Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) R → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) S)) % 5.83/6.02 False % 5.83/6.02 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Prop), % 5.83/6.02 Eq % 5.83/6.02 (Not % 5.83/6.02 (Exists fun S => % 5.83/6.02 Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) S))) % 5.83/6.02 True % 5.83/6.02 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Prop), % 5.83/6.02 Eq % 5.83/6.02 (Exists fun S => % 5.83/6.02 Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) S)) % 5.83/6.02 False % 5.83/6.02 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Prop), % 5.83/6.02 Eq (Iff (Iff (skS.0 0 a) (skS.0 1 a a_1)) (skS.0 2 a a_1 a_2) → Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) a_3)) False % 5.83/6.02 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Prop), Eq (Iff (skS.0 0 a) (Iff (skS.0 1 a a_1) a_2)) False % 5.83/6.02 Clause #31 (by clausification #[10]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) False) (Eq (Iff (skS.0 1 a a_1) a_2) False) % 5.83/6.02 Clause #32 (by clausification #[10]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) True) (Eq (Iff (skS.0 1 a a_1) a_2) True) % 5.83/6.02 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a a_1) False) (Eq a_2 False)) % 5.83/6.02 Clause #34 (by clausification #[31]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a a_1) True) (Eq a_2 True)) % 5.83/6.02 Clause #35 (by identity loobHoist #[33]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq a_2 False) (Or (Eq (skS.0 0 True) False) (Eq a False))) % 5.83/6.02 Clause #37 (by identity loobHoist #[35]): ∀ (a a_1 a_2 : Prop), % 5.83/6.02 Or (Eq a False) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a_1 True) False) (Eq a_2 False)))) % 5.83/6.02 Clause #39 (by identity loobHoist #[37]): ∀ (a a_1 a_2 : Prop), % 5.83/6.02 Or (Eq a False) % 5.83/6.02 (Or (Eq (skS.0 0 True) False) % 5.83/6.02 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 True True) False) (Eq a_1 False))))) % 5.83/6.02 Clause #41 (by eliminate duplicate literals #[39]): ∀ (a a_1 a_2 : Prop), % 5.83/6.02 Or (Eq a False) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) False)))) % 5.83/6.02 Clause #42 (by falseElim #[41]): ∀ (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))) % 5.83/6.02 Clause #43 (by identity loobHoist #[34]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq a_2 True) (Or (Eq (skS.0 0 True) False) (Eq a False))) % 5.83/6.02 Clause #45 (by identity loobHoist #[43]): ∀ (a a_1 a_2 : Prop), % 5.83/6.02 Or (Eq a True) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a_1 True) True) (Eq a_2 False)))) % 5.83/6.02 Clause #47 (by identity loobHoist #[45]): ∀ (a a_1 a_2 : Prop), % 5.83/6.02 Or (Eq a True) % 5.83/6.02 (Or (Eq (skS.0 0 True) False) % 5.83/6.02 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 True True) True) (Eq a_1 False))))) % 5.83/6.02 Clause #49 (by eliminate duplicate literals #[47]): ∀ (a a_1 a_2 : Prop), % 5.83/6.02 Or (Eq a True) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) True)))) % 5.83/6.02 Clause #50 (by clausification #[32]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) True) (Or (Eq (skS.0 1 a a_1) True) (Eq a_2 False)) % 5.83/6.02 Clause #51 (by clausification #[32]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 0 a) True) (Or (Eq (skS.0 1 a a_1) False) (Eq a_2 True)) % 5.83/6.08 Clause #52 (by identity loobHoist #[50]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq a_2 False) (Or (Eq (skS.0 0 True) True) (Eq a False))) % 5.83/6.08 Clause #54 (by identity loobHoist #[52]): ∀ (a a_1 a_2 : Prop), % 5.83/6.08 Or (Eq a False) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a_1 True) True) (Eq a_2 False)))) % 5.83/6.08 Clause #56 (by identity loobHoist #[54]): ∀ (a a_1 a_2 : Prop), % 5.83/6.08 Or (Eq a False) % 5.83/6.08 (Or (Eq (skS.0 0 True) True) % 5.83/6.08 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 True True) True) (Eq a_1 False))))) % 5.83/6.08 Clause #58 (by eliminate duplicate literals #[56]): ∀ (a a_1 a_2 : Prop), % 5.83/6.08 Or (Eq a False) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) True)))) % 5.83/6.08 Clause #59 (by falseElim #[58]): ∀ (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))) % 5.83/6.08 Clause #60 (by identity loobHoist #[51]): ∀ (a a_1 a_2 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq a_2 True) (Or (Eq (skS.0 0 True) True) (Eq a False))) % 5.83/6.08 Clause #62 (by identity loobHoist #[60]): ∀ (a a_1 a_2 : Prop), % 5.83/6.08 Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a_1 True) False) (Eq a_2 False)))) % 5.83/6.08 Clause #64 (by identity loobHoist #[62]): ∀ (a a_1 a_2 : Prop), % 5.83/6.08 Or (Eq a True) % 5.83/6.08 (Or (Eq (skS.0 0 True) True) % 5.83/6.08 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 True True) False) (Eq a_1 False))))) % 5.83/6.08 Clause #66 (by eliminate duplicate literals #[64]): ∀ (a a_1 a_2 : Prop), % 5.83/6.08 Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) False)))) % 5.83/6.08 Clause #67 (by falseElim #[66]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False))) % 5.83/6.08 Clause #90 (by falseElim #[67]): ∀ (a : Prop), Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) False)) % 5.83/6.08 Clause #111 (by falseElim #[59]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Eq (skS.0 1 True True) True)) % 5.83/6.08 Clause #112 (by falseElim #[111]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) True) % 5.83/6.08 Clause #113 (by superposition #[112, 90]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a True) (Or (Eq (skS.0 0 True) True) (Eq True False))) % 5.83/6.08 Clause #114 (by clausification #[113]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a True) (Eq (skS.0 0 True) True)) % 5.83/6.08 Clause #115 (by eliminate duplicate literals #[114]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Eq a True) % 5.83/6.08 Clause #118 (by equality factoring #[115]): Or (Ne True True) (Eq (skS.0 0 True) True) % 5.83/6.08 Clause #120 (by clausification #[118]): Or (Eq (skS.0 0 True) True) (Or (Eq True False) (Eq True False)) % 5.83/6.08 Clause #122 (by clausification #[120]): Or (Eq (skS.0 0 True) True) (Eq True False) % 5.83/6.08 Clause #123 (by clausification #[122]): Eq (skS.0 0 True) True % 5.83/6.08 Clause #124 (by backward demodulation #[123, 49]): ∀ (a a_1 a_2 : Prop), % 5.83/6.08 Or (Eq a True) (Or (Eq True False) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) True)))) % 5.83/6.08 Clause #125 (by backward demodulation #[123, 42]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False))) % 5.83/6.08 Clause #130 (by clausification #[125]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq a_1 False) (Eq (skS.0 1 True True) False)) % 5.83/6.08 Clause #132 (by falseElim #[130]): ∀ (a : Prop), Or (Eq a False) (Eq (skS.0 1 True True) False) % 5.83/6.08 Clause #134 (by falseElim #[132]): Eq (skS.0 1 True True) False % 5.83/6.08 Clause #143 (by clausification #[124]): ∀ (a a_1 a_2 : Prop), Or (Eq a True) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 True True) True))) % 5.83/6.08 Clause #145 (by falseElim #[143]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq a_1 False) (Eq (skS.0 1 True True) True)) % 5.83/6.08 Clause #147 (by falseElim #[145]): ∀ (a : Prop), Or (Eq a True) (Eq (skS.0 1 True True) True) % 5.83/6.08 Clause #149 (by superposition #[147, 134]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 5.83/6.08 Clause #152 (by clausification #[149]): ∀ (a : Prop), Eq a True % 5.83/6.08 Clause #154 (by falseElim #[152]): False % 5.83/6.08 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------