%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO007^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:08:24 PM UTC 2025 % Result : Theorem 4.81s 4.99s % Output : Proof 4.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SYO007^1 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n021.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 13:02:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.81/4.99 SZS status Theorem for theBenchmark.p % 4.81/4.99 SZS output start Proof for theBenchmark.p % 4.81/4.99 Clause #0 (by assumption #[]): Eq (Eq leibeq fun U V => ∀ (Q : Prop → Prop), Q U → Q V) True % 4.81/4.99 Clause #1 (by assumption #[]): Eq (Not (∀ (A B : Prop), Iff A B → leibeq A B)) True % 4.81/4.99 Clause #2 (by clausification #[1]): Eq (∀ (A B : Prop), Iff A B → leibeq A B) False % 4.81/4.99 Clause #3 (by clausification #[2]): ∀ (a : Prop), Eq (Not (∀ (B : Prop), Iff (skS.0 0 a) B → leibeq (skS.0 0 a) B)) True % 4.81/4.99 Clause #4 (by clausification #[3]): ∀ (a : Prop), Eq (∀ (B : Prop), Iff (skS.0 0 a) B → leibeq (skS.0 0 a) B) False % 4.81/4.99 Clause #5 (by clausification #[4]): ∀ (a a_1 : Prop), Eq (Not (Iff (skS.0 0 a) (skS.0 1 a a_1) → leibeq (skS.0 0 a) (skS.0 1 a a_1))) True % 4.81/4.99 Clause #6 (by clausification #[5]): ∀ (a a_1 : Prop), Eq (Iff (skS.0 0 a) (skS.0 1 a a_1) → leibeq (skS.0 0 a) (skS.0 1 a a_1)) False % 4.81/4.99 Clause #7 (by clausification #[6]): ∀ (a a_1 : Prop), Eq (Iff (skS.0 0 a) (skS.0 1 a a_1)) True % 4.81/4.99 Clause #8 (by clausification #[6]): ∀ (a a_1 : Prop), Eq (leibeq (skS.0 0 a) (skS.0 1 a a_1)) False % 4.81/4.99 Clause #9 (by clausification #[7]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) True) (Eq (skS.0 1 a a_1) False) % 4.81/4.99 Clause #10 (by clausification #[7]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) False) (Eq (skS.0 1 a a_1) True) % 4.81/4.99 Clause #11 (by identity loobHoist #[9]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq (skS.0 0 True) True) (Eq a False)) % 4.81/4.99 Clause #13 (by identity loobHoist #[11]): ∀ (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))) % 4.81/4.99 Clause #15 (by identity loobHoist #[13]): ∀ (a a_1 : Prop), % 4.81/4.99 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)))) % 4.81/4.99 Clause #17 (by eliminate duplicate literals #[15]): ∀ (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))) % 4.81/4.99 Clause #18 (by falseElim #[17]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Eq (skS.0 1 True True) False)) % 4.81/4.99 Clause #19 (by clausification #[0]): Eq leibeq fun U V => ∀ (Q : Prop → Prop), Q U → Q V % 4.81/4.99 Clause #20 (by argument congruence #[19]): ∀ (a : Prop), Eq (leibeq a) ((fun U V => ∀ (Q : Prop → Prop), Q U → Q V) a) % 4.81/4.99 Clause #22 (by betaEtaReduce #[20]): ∀ (a : Prop), Eq (leibeq a) fun V => ∀ (Q : Prop → Prop), Q a → Q V % 4.81/4.99 Clause #23 (by identity loobHoist #[22]): ∀ (a : Prop), Or (Eq (leibeq True) fun V => ∀ (Q : Prop → Prop), Q a → Q V) (Eq a False) % 4.81/4.99 Clause #24 (by identity boolHoist #[22]): ∀ (a : Prop), Or (Eq (leibeq False) fun V => ∀ (Q : Prop → Prop), Q a → Q V) (Eq a True) % 4.81/4.99 Clause #25 (by falseElim #[23]): Eq (leibeq True) fun V => ∀ (Q : Prop → Prop), Q True → Q V % 4.81/4.99 Clause #26 (by argument congruence #[25]): ∀ (a : Prop), Eq (leibeq True a) ((fun V => ∀ (Q : Prop → Prop), Q True → Q V) a) % 4.81/4.99 Clause #27 (by betaEtaReduce #[26]): ∀ (a : Prop), Eq (leibeq True a) (∀ (Q : Prop → Prop), Q True → Q a) % 4.81/4.99 Clause #28 (by identity loobHoist #[27]): ∀ (a : Prop), Or (Eq (leibeq True True) (∀ (Q : Prop → Prop), Q True → Q a)) (Eq a False) % 4.81/4.99 Clause #30 (by falseElim #[28]): Eq (leibeq True True) (∀ (Q : Prop → Prop), Q True → Q True) % 4.81/4.99 Clause #31 (by identity loobHoist #[8]): ∀ (a a_1 : Prop), Or (Eq (leibeq (skS.0 0 a) True) False) (Eq (skS.0 1 a a_1) False) % 4.81/4.99 Clause #32 (by identity boolHoist #[8]): ∀ (a a_1 : Prop), Or (Eq (leibeq (skS.0 0 a) False) False) (Eq (skS.0 1 a a_1) True) % 4.81/4.99 Clause #33 (by identity loobHoist #[31]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) False) (Or (Eq (leibeq True True) False) (Eq (skS.0 0 a) False)) % 4.81/4.99 Clause #36 (by identity boolHoist #[33]): ∀ (a a_1 : Prop), % 4.81/4.99 Or (Eq (leibeq True True) False) (Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a False) False) (Eq a_1 True))) % 4.81/4.99 Clause #42 (by bool simp #[30]): Eq (leibeq True True) True % 4.81/4.99 Clause #52 (by argument congruence #[24]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) ((fun V => ∀ (Q : Prop → Prop), Q a_1 → Q V) a)) (Eq a_1 True) % 4.81/4.99 Clause #56 (by identity loobHoist #[10]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq (skS.0 0 True) False) (Eq a False)) % 4.81/5.02 Clause #59 (by identity boolHoist #[56]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq (skS.0 1 a False) True) (Eq a_1 True))) % 4.81/5.02 Clause #99 (by betaEtaReduce #[52]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) (∀ (Q : Prop → Prop), Q a_1 → Q a)) (Eq a_1 True) % 4.81/5.02 Clause #101 (by identity boolHoist #[99]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a_1)) (Eq a_1 True)) % 4.81/5.02 Clause #113 (by equality factoring #[101]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a)) (Or (Ne True True) (Eq a True)) % 4.81/5.02 Clause #122 (by clausification #[113]): ∀ (a : Prop), % 4.81/5.02 Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a)) (Or (Eq a True) (Or (Eq True False) (Eq True False))) % 4.81/5.02 Clause #124 (by clausification #[122]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a)) (Or (Eq a True) (Eq True False)) % 4.81/5.02 Clause #125 (by clausification #[124]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (Q : Prop → Prop), Q a → Q a)) (Eq a True) % 4.81/5.02 Clause #126 (by bool simp #[125]): ∀ (a : Prop), Or (Eq (leibeq False False) True) (Eq a True) % 4.81/5.02 Clause #128 (by equality factoring #[126]): Or (Ne True True) (Eq (leibeq False False) True) % 4.81/5.02 Clause #130 (by clausification #[128]): Or (Eq (leibeq False False) True) (Or (Eq True False) (Eq True False)) % 4.81/5.02 Clause #132 (by clausification #[130]): Or (Eq (leibeq False False) True) (Eq True False) % 4.81/5.02 Clause #133 (by clausification #[132]): Eq (leibeq False False) True % 4.81/5.02 Clause #143 (by falseElim #[18]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) False) % 4.81/5.02 Clause #164 (by identity boolHoist #[32]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq (leibeq False False) False) (Eq (skS.0 0 a) True)) % 4.81/5.02 Clause #195 (by forward demodulation #[36, 42]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a False) False) (Eq a_1 True))) % 4.81/5.02 Clause #196 (by clausification #[195]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) False) (Or (Eq (skS.0 1 a False) False) (Eq a_1 True)) % 4.81/5.02 Clause #197 (by identity loobHoist #[196]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a False) False) (Or (Eq a_1 True) (Or (Eq (skS.0 0 True) False) (Eq a False))) % 4.81/5.02 Clause #199 (by identity loobHoist #[197]): ∀ (a a_1 : Prop), % 4.81/5.02 Or (Eq a True) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 True False) False) (Eq a_1 False)))) % 4.81/5.02 Clause #201 (by eliminate duplicate literals #[199]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (skS.0 0 True) False) (Or (Eq a_1 False) (Eq (skS.0 1 True False) False))) % 4.81/5.02 Clause #253 (by identity loobHoist #[59]): ∀ (a a_1 : Prop), % 4.81/5.02 Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq a_1 True) (Or (Eq (skS.0 1 True False) True) (Eq a False)))) % 4.81/5.02 Clause #255 (by eliminate duplicate literals #[253]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 True) False) (Or (Eq a False) (Or (Eq a_1 True) (Eq (skS.0 1 True False) True))) % 4.81/5.02 Clause #326 (by forward demodulation #[164, 133]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Or (Eq True False) (Eq (skS.0 0 a) True)) % 4.81/5.02 Clause #327 (by clausification #[326]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a a_1) True) (Eq (skS.0 0 a) True) % 4.81/5.02 Clause #328 (by identity loobHoist #[327]): ∀ (a a_1 : Prop), Or (Eq (skS.0 0 a) True) (Or (Eq (skS.0 1 a True) True) (Eq a_1 False)) % 4.81/5.02 Clause #330 (by identity loobHoist #[328]): ∀ (a a_1 : Prop), Or (Eq (skS.0 1 a True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 0 True) True) (Eq a False))) % 4.81/5.02 Clause #332 (by identity loobHoist #[330]): ∀ (a a_1 : Prop), % 4.81/5.02 Or (Eq a False) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 1 True True) True) (Eq a_1 False)))) % 4.81/5.02 Clause #334 (by eliminate duplicate literals #[332]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq (skS.0 0 True) True) (Or (Eq a_1 False) (Eq (skS.0 1 True True) True))) % 4.81/5.02 Clause #338 (by falseElim #[334]): ∀ (a : Prop), Or (Eq (skS.0 0 True) True) (Or (Eq a False) (Eq (skS.0 1 True True) True)) % 4.81/5.02 Clause #342 (by falseElim #[338]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 1 True True) True) % 4.81/5.03 Clause #343 (by superposition #[342, 143]): Or (Eq (skS.0 0 True) True) (Or (Eq (skS.0 0 True) True) (Eq True False)) % 4.81/5.03 Clause #349 (by clausification #[343]): Or (Eq (skS.0 0 True) True) (Eq (skS.0 0 True) True) % 4.81/5.03 Clause #350 (by eliminate duplicate literals #[349]): Eq (skS.0 0 True) True % 4.81/5.03 Clause #352 (by backward demodulation #[350, 201]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq True False) (Or (Eq a_1 False) (Eq (skS.0 1 True False) False))) % 4.81/5.03 Clause #356 (by backward demodulation #[350, 255]): ∀ (a a_1 : Prop), Or (Eq True False) (Or (Eq a False) (Or (Eq a_1 True) (Eq (skS.0 1 True False) True))) % 4.81/5.03 Clause #365 (by clausification #[356]): ∀ (a a_1 : Prop), Or (Eq a False) (Or (Eq a_1 True) (Eq (skS.0 1 True False) True)) % 4.81/5.03 Clause #369 (by falseElim #[365]): ∀ (a : Prop), Or (Eq a True) (Eq (skS.0 1 True False) True) % 4.81/5.03 Clause #374 (by equality factoring #[369]): Or (Ne True True) (Eq (skS.0 1 True False) True) % 4.81/5.03 Clause #375 (by clausification #[374]): Or (Eq (skS.0 1 True False) True) (Or (Eq True False) (Eq True False)) % 4.81/5.03 Clause #377 (by clausification #[375]): Or (Eq (skS.0 1 True False) True) (Eq True False) % 4.81/5.03 Clause #378 (by clausification #[377]): Eq (skS.0 1 True False) True % 4.81/5.03 Clause #380 (by clausification #[352]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq a_1 False) (Eq (skS.0 1 True False) False)) % 4.81/5.03 Clause #384 (by falseElim #[380]): ∀ (a : Prop), Or (Eq a True) (Eq (skS.0 1 True False) False) % 4.81/5.03 Clause #385 (by superposition #[384, 378]): ∀ (a : Prop), Or (Eq a True) (Eq False True) % 4.81/5.03 Clause #389 (by clausification #[385]): ∀ (a : Prop), Eq a True % 4.81/5.03 Clause #391 (by falseElim #[389]): False % 4.81/5.03 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------