%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU807^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 08:02:29 PM UTC 2025 % Result : Theorem 74.28s 74.47s % Output : Proof 74.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU807^2 : TPTP v9.2.0. Released v3.7.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n025.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 06:16:08 EDT 2025 % 0.13/0.34 % CPUTime : % 74.28/74.47 SZS status Theorem for theBenchmark.p % 74.28/74.47 SZS output start Proof for theBenchmark.p % 74.28/74.47 Clause #0 (by assumption #[]): Eq % 74.28/74.47 (Eq foundationAx % 74.28/74.47 (∀ (A : Iota), % 74.28/74.47 (Exists fun Xx => in Xx A) → Exists fun B => And (in B A) (Not (Exists fun Xx => And (in Xx B) (in Xx A))))) % 74.28/74.47 True % 74.28/74.47 Clause #1 (by assumption #[]): Eq (Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))) True % 74.28/74.47 Clause #2 (by assumption #[]): Eq (Eq setadjoinIR (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A))) True % 74.28/74.47 Clause #4 (by assumption #[]): Eq (Eq upairset2E (∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy))) True % 74.28/74.47 Clause #5 (by assumption #[]): Eq (Not (foundationAx → setadjoinIL → setadjoinIR → in__Cong → upairset2E → ∀ (A B : Iota), in A B → Not (in B A))) True % 74.28/74.47 Clause #6 (by clausification #[1]): Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 74.28/74.47 Clause #8 (by clausify Prop equality #[6]): Or (Eq setadjoinIL False) (Eq (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) True) % 74.28/74.47 Clause #10 (by clausification #[8]): ∀ (a : Iota), Or (Eq setadjoinIL False) (Eq (∀ (Xy : Iota), in a (setadjoin a Xy)) True) % 74.28/74.47 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq setadjoinIL False) (Eq (in a (setadjoin a a_1)) True) % 74.28/74.47 Clause #16 (by clausification #[2]): Eq setadjoinIR (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A)) % 74.28/74.47 Clause #20 (by clausification #[0]): Eq foundationAx % 74.28/74.47 (∀ (A : Iota), % 74.28/74.47 (Exists fun Xx => in Xx A) → Exists fun B => And (in B A) (Not (Exists fun Xx => And (in Xx B) (in Xx A)))) % 74.28/74.47 Clause #22 (by clausify Prop equality #[20]): Or (Eq foundationAx False) % 74.28/74.47 (Eq % 74.28/74.47 (∀ (A : Iota), % 74.28/74.47 (Exists fun Xx => in Xx A) → Exists fun B => And (in B A) (Not (Exists fun Xx => And (in Xx B) (in Xx A)))) % 74.28/74.47 True) % 74.28/74.47 Clause #36 (by clausification #[5]): Eq (foundationAx → setadjoinIL → setadjoinIR → in__Cong → upairset2E → ∀ (A B : Iota), in A B → Not (in B A)) False % 74.28/74.47 Clause #37 (by clausification #[36]): Eq foundationAx True % 74.28/74.47 Clause #38 (by clausification #[36]): Eq (setadjoinIL → setadjoinIR → in__Cong → upairset2E → ∀ (A B : Iota), in A B → Not (in B A)) False % 74.28/74.47 Clause #40 (by clausification #[38]): Eq setadjoinIL True % 74.28/74.47 Clause #41 (by clausification #[38]): Eq (setadjoinIR → in__Cong → upairset2E → ∀ (A B : Iota), in A B → Not (in B A)) False % 74.28/74.47 Clause #43 (by backward demodulation #[40, 11]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a a_1)) True) % 74.28/74.47 Clause #49 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a a_1)) True % 74.28/74.47 Clause #51 (by clausification #[41]): Eq setadjoinIR True % 74.28/74.47 Clause #52 (by clausification #[41]): Eq (in__Cong → upairset2E → ∀ (A B : Iota), in A B → Not (in B A)) False % 74.28/74.47 Clause #53 (by backward demodulation #[51, 16]): Eq True (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A)) % 74.28/74.47 Clause #56 (by clausification #[53]): ∀ (a : Iota), Eq (∀ (A Xy : Iota), in Xy A → in Xy (setadjoin a A)) True % 74.28/74.47 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), Eq (∀ (Xy : Iota), in Xy a → in Xy (setadjoin a_1 a)) True % 74.28/74.47 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (setadjoin a_2 a_1)) True % 74.28/74.47 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (setadjoin a_2 a_1)) True) % 74.28/74.47 Clause #60 (by superposition #[59, 49]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 (setadjoin a a_2))) True) (Eq False True) % 74.28/74.47 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Eq (in a (setadjoin a_1 (setadjoin a a_2))) True % 74.28/74.47 Clause #63 (by clausification #[4]): Eq upairset2E (∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy)) % 74.28/74.47 Clause #68 (by clausification #[52]): Eq (upairset2E → ∀ (A B : Iota), in A B → Not (in B A)) False % 74.28/74.47 Clause #70 (by clausification #[68]): Eq upairset2E True % 74.28/74.47 Clause #71 (by clausification #[68]): Eq (∀ (A B : Iota), in A B → Not (in B A)) False % 74.28/74.47 Clause #72 (by backward demodulation #[70, 63]): Eq True (∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy)) % 74.28/74.50 Clause #73 (by clausification #[71]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), in (skS.0 5 a) B → Not (in B (skS.0 5 a)))) True % 74.28/74.50 Clause #74 (by clausification #[73]): ∀ (a : Iota), Eq (∀ (B : Iota), in (skS.0 5 a) B → Not (in B (skS.0 5 a))) False % 74.28/74.50 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 5 a) (skS.0 6 a a_1) → Not (in (skS.0 6 a a_1) (skS.0 5 a)))) True % 74.28/74.50 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a) (skS.0 6 a a_1) → Not (in (skS.0 6 a a_1) (skS.0 5 a))) False % 74.28/74.50 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a) (skS.0 6 a a_1)) True % 74.28/74.50 Clause #78 (by clausification #[76]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 6 a a_1) (skS.0 5 a))) False % 74.28/74.50 Clause #104 (by clausification #[72]): ∀ (a : Iota), Eq (∀ (Xy Xz : Iota), in Xz (setadjoin a (setadjoin Xy emptyset)) → Or (Eq Xz a) (Eq Xz Xy)) True % 74.28/74.50 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (∀ (Xz : Iota), in Xz (setadjoin a (setadjoin a_1 emptyset)) → Or (Eq Xz a) (Eq Xz a_1)) True % 74.28/74.50 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset)) → Or (Eq a a_1) (Eq a a_2)) True % 74.28/74.50 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset))) False) (Eq (Or (Eq a a_1) (Eq a a_2)) True) % 74.28/74.50 Clause #108 (by clausification #[107]): ∀ (a a_1 a_2 : Iota), % 74.28/74.50 Or (Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset))) False) (Or (Eq (Eq a a_1) True) (Eq (Eq a a_2) True)) % 74.28/74.50 Clause #109 (by clausification #[108]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset))) False) (Or (Eq (Eq a a_2) True) (Eq a a_1)) % 74.28/74.50 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 (setadjoin a_2 emptyset))) False) (Or (Eq a a_1) (Eq a a_2)) % 74.28/74.50 Clause #114 (by clausification #[22]): ∀ (a : Iota), % 74.28/74.50 Or (Eq foundationAx False) % 74.28/74.50 (Eq ((Exists fun Xx => in Xx a) → Exists fun B => And (in B a) (Not (Exists fun Xx => And (in Xx B) (in Xx a)))) % 74.28/74.50 True) % 74.28/74.50 Clause #115 (by clausification #[114]): ∀ (a : Iota), % 74.28/74.50 Or (Eq foundationAx False) % 74.28/74.50 (Or (Eq (Exists fun Xx => in Xx a) False) % 74.28/74.50 (Eq (Exists fun B => And (in B a) (Not (Exists fun Xx => And (in Xx B) (in Xx a)))) True)) % 74.28/74.50 Clause #116 (by clausification #[115]): ∀ (a a_1 : Iota), % 74.28/74.50 Or (Eq foundationAx False) % 74.28/74.50 (Or (Eq (Exists fun B => And (in B a) (Not (Exists fun Xx => And (in Xx B) (in Xx a)))) True) (Eq (in a_1 a) False)) % 74.28/74.50 Clause #117 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), % 74.28/74.50 Or (Eq foundationAx False) % 74.28/74.50 (Or (Eq (in a a_1) False) % 74.28/74.50 (Eq (And (in (skS.0 9 a_1 a_2) a_1) (Not (Exists fun Xx => And (in Xx (skS.0 9 a_1 a_2)) (in Xx a_1)))) True)) % 74.28/74.50 Clause #118 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), % 74.28/74.50 Or (Eq foundationAx False) % 74.28/74.50 (Or (Eq (in a a_1) False) (Eq (Not (Exists fun Xx => And (in Xx (skS.0 9 a_1 a_2)) (in Xx a_1))) True)) % 74.28/74.50 Clause #119 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), Or (Eq foundationAx False) (Or (Eq (in a a_1) False) (Eq (in (skS.0 9 a_1 a_2) a_1) True)) % 74.28/74.50 Clause #120 (by clausification #[118]): ∀ (a a_1 a_2 : Iota), % 74.28/74.50 Or (Eq foundationAx False) % 74.28/74.50 (Or (Eq (in a a_1) False) (Eq (Exists fun Xx => And (in Xx (skS.0 9 a_1 a_2)) (in Xx a_1)) False)) % 74.28/74.50 Clause #121 (by clausification #[120]): ∀ (a a_1 a_2 a_3 : Iota), % 74.28/74.50 Or (Eq foundationAx False) (Or (Eq (in a a_1) False) (Eq (And (in a_2 (skS.0 9 a_1 a_3)) (in a_2 a_1)) False)) % 74.28/74.50 Clause #122 (by clausification #[121]): ∀ (a a_1 a_2 a_3 : Iota), % 74.28/74.50 Or (Eq foundationAx False) % 74.28/74.50 (Or (Eq (in a a_1) False) (Or (Eq (in a_2 (skS.0 9 a_1 a_3)) False) (Eq (in a_2 a_1) False))) % 74.28/74.50 Clause #123 (by forward demodulation #[122, 37]): ∀ (a a_1 a_2 a_3 : Iota), % 74.28/74.50 Or (Eq True False) (Or (Eq (in a a_1) False) (Or (Eq (in a_2 (skS.0 9 a_1 a_3)) False) (Eq (in a_2 a_1) False))) % 74.28/74.50 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 (skS.0 9 a_1 a_3)) False) (Eq (in a_2 a_1) False)) % 74.36/74.54 Clause #173 (by clausification #[78]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 5 a)) True % 74.36/74.54 Clause #177 (by forward demodulation #[119, 37]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a a_1) False) (Eq (in (skS.0 9 a_1 a_2) a_1) True)) % 74.36/74.54 Clause #178 (by clausification #[177]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in (skS.0 9 a_1 a_2) a_1) True) % 74.36/74.54 Clause #181 (by superposition #[178, 49]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 9 (setadjoin a a_1) a_2) (setadjoin a a_1)) True) (Eq False True) % 74.36/74.54 Clause #186 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 9 (setadjoin a a_1) a_2) (setadjoin a a_1)) True % 74.36/74.54 Clause #187 (by superposition #[186, 110]): ∀ (a a_1 a_2 : Iota), % 74.36/74.54 Or (Eq True False) % 74.36/74.54 (Or (Eq (skS.0 9 (setadjoin a (setadjoin a_1 emptyset)) a_2) a) % 74.36/74.54 (Eq (skS.0 9 (setadjoin a (setadjoin a_1 emptyset)) a_2) a_1)) % 74.36/74.54 Clause #189 (by superposition #[186, 124]): ∀ (a a_1 a_2 a_3 : Iota), % 74.36/74.54 Or (Eq True False) (Or (Eq (in a (skS.0 9 (setadjoin a_1 a_2) a_3)) False) (Eq (in a (setadjoin a_1 a_2)) False)) % 74.36/74.54 Clause #264 (by clausification #[189]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 9 (setadjoin a_1 a_2) a_3)) False) (Eq (in a (setadjoin a_1 a_2)) False) % 74.36/74.54 Clause #583 (by clausification #[187]): ∀ (a a_1 a_2 : Iota), % 74.36/74.54 Or (Eq (skS.0 9 (setadjoin a (setadjoin a_1 emptyset)) a_2) a) % 74.36/74.54 (Eq (skS.0 9 (setadjoin a (setadjoin a_1 emptyset)) a_2) a_1) % 74.36/74.54 Clause #595 (by superposition #[583, 264]): ∀ (a a_1 a_2 a_3 : Iota), % 74.36/74.54 Or (Eq (skS.0 9 (setadjoin a (setadjoin a_1 emptyset)) a_2) a) % 74.36/74.54 (Or (Eq (in a_3 a_1) False) (Eq (in a_3 (setadjoin a (setadjoin a_1 emptyset))) False)) % 74.36/74.54 Clause #671 (by superposition #[595, 77]): ∀ (a a_1 a_2 a_3 : Iota), % 74.36/74.54 Or (Eq (skS.0 9 (setadjoin a (setadjoin (skS.0 6 a_1 a_2) emptyset)) a_3) a) % 74.36/74.54 (Or (Eq (in (skS.0 5 a_1) (setadjoin a (setadjoin (skS.0 6 a_1 a_2) emptyset))) False) (Eq False True)) % 74.36/74.54 Clause #2566 (by clausification #[671]): ∀ (a a_1 a_2 a_3 : Iota), % 74.36/74.54 Or (Eq (skS.0 9 (setadjoin a (setadjoin (skS.0 6 a_1 a_2) emptyset)) a_3) a) % 74.36/74.54 (Eq (in (skS.0 5 a_1) (setadjoin a (setadjoin (skS.0 6 a_1 a_2) emptyset))) False) % 74.36/74.54 Clause #2567 (by superposition #[2566, 49]): ∀ (a a_1 a_2 : Iota), % 74.36/74.54 Or (Eq (skS.0 9 (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_1) emptyset)) a_2) (skS.0 5 a)) (Eq False True) % 74.36/74.54 Clause #2568 (by clausification #[2567]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 9 (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_1) emptyset)) a_2) (skS.0 5 a) % 74.36/74.54 Clause #2572 (by superposition #[2568, 264]): ∀ (a a_1 a_2 : Iota), % 74.36/74.54 Or (Eq (in a (skS.0 5 a_1)) False) (Eq (in a (setadjoin (skS.0 5 a_1) (setadjoin (skS.0 6 a_1 a_2) emptyset))) False) % 74.36/74.54 Clause #2612 (by superposition #[2572, 173]): ∀ (a a_1 a_2 : Iota), % 74.36/74.54 Or (Eq (in (skS.0 6 a a_1) (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_2) emptyset))) False) (Eq False True) % 74.36/74.54 Clause #2615 (by clausification #[2612]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1) (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_2) emptyset))) False % 74.36/74.54 Clause #2616 (by superposition #[2615, 61]): Eq False True % 74.36/74.54 Clause #2617 (by clausification #[2616]): False % 74.36/74.54 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------