%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU107+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.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 08:00:52 PM UTC 2025 % Result : Theorem 86.70s 86.88s % Output : Proof 86.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU107+1 : TPTP v9.2.0. Released v3.2.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n010.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 05:13:23 EDT 2025 % 0.13/0.34 % CPUTime : % 86.70/86.88 SZS status Theorem for theBenchmark.p % 86.70/86.88 SZS output start Proof for theBenchmark.p % 86.70/86.88 Clause #5 (by assumption #[]): Eq % 86.70/86.88 (∀ (A B C : Iota), % 86.70/86.88 And (And (And (Not (empty A)) (preboolean A)) (element B A)) (element C A) → element (prebool_difference A B C) A) % 86.70/86.88 True % 86.70/86.88 Clause #6 (by assumption #[]): Eq (∀ (A : Iota), Exists fun B => element B A) True % 86.70/86.88 Clause #18 (by assumption #[]): Eq % 86.70/86.88 (∀ (A B C : Iota), % 86.70/86.88 And (And (And (Not (empty A)) (preboolean A)) (element B A)) (element C A) → % 86.70/86.88 Eq (prebool_difference A B C) (set_difference B C)) % 86.70/86.88 True % 86.70/86.88 Clause #19 (by assumption #[]): Eq (∀ (A : Iota), Iota → subset A A) True % 86.70/86.88 Clause #20 (by assumption #[]): Eq (Not (∀ (A : Iota), And (Not (empty A)) (preboolean A) → in empty_set A)) True % 86.70/86.88 Clause #22 (by assumption #[]): Eq (∀ (A B : Iota), element A B → Or (empty B) (in A B)) True % 86.70/86.88 Clause #23 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A B) empty_set) (subset A B)) True % 86.70/86.88 Clause #48 (by clausification #[19]): ∀ (a : Iota), Eq (Iota → subset a a) True % 86.70/86.88 Clause #49 (by clausification #[48]): ∀ (a : Iota), Iota → Eq (subset a a) True % 86.70/86.88 Clause #55 (by clausification #[20]): Eq (∀ (A : Iota), And (Not (empty A)) (preboolean A) → in empty_set A) False % 86.70/86.88 Clause #56 (by clausification #[55]): ∀ (a : Iota), Eq (Not (And (Not (empty (skS.0 2 a))) (preboolean (skS.0 2 a)) → in empty_set (skS.0 2 a))) True % 86.70/86.88 Clause #57 (by clausification #[56]): ∀ (a : Iota), Eq (And (Not (empty (skS.0 2 a))) (preboolean (skS.0 2 a)) → in empty_set (skS.0 2 a)) False % 86.70/86.88 Clause #58 (by clausification #[57]): ∀ (a : Iota), Eq (And (Not (empty (skS.0 2 a))) (preboolean (skS.0 2 a))) True % 86.70/86.88 Clause #59 (by clausification #[57]): ∀ (a : Iota), Eq (in empty_set (skS.0 2 a)) False % 86.70/86.88 Clause #60 (by clausification #[58]): ∀ (a : Iota), Eq (preboolean (skS.0 2 a)) True % 86.70/86.88 Clause #61 (by clausification #[58]): ∀ (a : Iota), Eq (Not (empty (skS.0 2 a))) True % 86.70/86.88 Clause #83 (by clausification #[5]): ∀ (a : Iota), % 86.70/86.88 Eq % 86.70/86.88 (∀ (B C : Iota), % 86.70/86.88 And (And (And (Not (empty a)) (preboolean a)) (element B a)) (element C a) → element (prebool_difference a B C) a) % 86.70/86.88 True % 86.70/86.88 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), % 86.70/86.88 Eq % 86.70/86.88 (∀ (C : Iota), % 86.70/86.88 And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element C a) → % 86.70/86.88 element (prebool_difference a a_1 C) a) % 86.70/86.88 True % 86.70/86.88 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), % 86.70/86.88 Eq % 86.70/86.88 (And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element a_2 a) → % 86.70/86.88 element (prebool_difference a a_1 a_2) a) % 86.70/86.88 True % 86.70/86.88 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), % 86.70/86.88 Or (Eq (And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element a_2 a)) False) % 86.70/86.88 (Eq (element (prebool_difference a a_1 a_2) a) True) % 86.70/86.88 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), % 86.70/86.88 Or (Eq (element (prebool_difference a a_1 a_2) a) True) % 86.70/86.88 (Or (Eq (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) False) (Eq (element a_2 a) False)) % 86.70/86.88 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), % 86.70/86.88 Or (Eq (element (prebool_difference a a_1 a_2) a) True) % 86.70/86.88 (Or (Eq (element a_2 a) False) (Or (Eq (And (Not (empty a)) (preboolean a)) False) (Eq (element a_1 a) False))) % 86.70/86.88 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), % 86.70/86.88 Or (Eq (element (prebool_difference a a_1 a_2) a) True) % 86.70/86.88 (Or (Eq (element a_2 a) False) % 86.70/86.88 (Or (Eq (element a_1 a) False) (Or (Eq (Not (empty a)) False) (Eq (preboolean a) False)))) % 86.70/86.88 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), % 86.70/86.88 Or (Eq (element (prebool_difference a a_1 a_2) a) True) % 86.70/86.88 (Or (Eq (element a_2 a) False) (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Eq (empty a) True)))) % 86.70/86.88 Clause #94 (by clausification #[6]): ∀ (a : Iota), Eq (Exists fun B => element B a) True % 86.70/86.88 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Eq (element (skS.0 3 a a_1) a) True % 86.70/86.88 Clause #96 (by superposition #[95, 90]): ∀ (a a_1 a_2 : Iota), % 86.70/86.88 Or (Eq (element (prebool_difference a a_1 (skS.0 3 a a_2)) a) True) % 86.70/86.88 (Or (Eq True False) (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Eq (empty a) True)))) % 86.70/86.90 Clause #111 (by clausification #[61]): ∀ (a : Iota), Eq (empty (skS.0 2 a)) False % 86.70/86.90 Clause #137 (by clausification #[22]): ∀ (a : Iota), Eq (∀ (B : Iota), element a B → Or (empty B) (in a B)) True % 86.70/86.90 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota), Eq (element a a_1 → Or (empty a_1) (in a a_1)) True % 86.70/86.90 Clause #139 (by clausification #[138]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Eq (Or (empty a_1) (in a a_1)) True) % 86.70/86.90 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), Or (Eq (element a a_1) False) (Or (Eq (empty a_1) True) (Eq (in a a_1) True)) % 86.70/86.90 Clause #198 (by clausification #[18]): ∀ (a : Iota), % 86.70/86.90 Eq % 86.70/86.90 (∀ (B C : Iota), % 86.70/86.90 And (And (And (Not (empty a)) (preboolean a)) (element B a)) (element C a) → % 86.70/86.90 Eq (prebool_difference a B C) (set_difference B C)) % 86.70/86.90 True % 86.70/86.90 Clause #199 (by clausification #[198]): ∀ (a a_1 : Iota), % 86.70/86.90 Eq % 86.70/86.90 (∀ (C : Iota), % 86.70/86.90 And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element C a) → % 86.70/86.90 Eq (prebool_difference a a_1 C) (set_difference a_1 C)) % 86.70/86.90 True % 86.70/86.90 Clause #200 (by clausification #[199]): ∀ (a a_1 a_2 : Iota), % 86.70/86.90 Eq % 86.70/86.90 (And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element a_2 a) → % 86.70/86.90 Eq (prebool_difference a a_1 a_2) (set_difference a_1 a_2)) % 86.70/86.90 True % 86.70/86.90 Clause #201 (by clausification #[200]): ∀ (a a_1 a_2 : Iota), % 86.70/86.90 Or (Eq (And (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) (element a_2 a)) False) % 86.70/86.90 (Eq (Eq (prebool_difference a a_1 a_2) (set_difference a_1 a_2)) True) % 86.70/86.90 Clause #202 (by clausification #[201]): ∀ (a a_1 a_2 : Iota), % 86.70/86.90 Or (Eq (Eq (prebool_difference a a_1 a_2) (set_difference a_1 a_2)) True) % 86.70/86.90 (Or (Eq (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) False) (Eq (element a_2 a) False)) % 86.70/86.90 Clause #203 (by clausification #[202]): ∀ (a a_1 a_2 : Iota), % 86.70/86.90 Or (Eq (And (And (Not (empty a)) (preboolean a)) (element a_1 a)) False) % 86.70/86.90 (Or (Eq (element a_2 a) False) (Eq (prebool_difference a a_1 a_2) (set_difference a_1 a_2))) % 86.70/86.90 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota), % 86.70/86.90 Or (Eq (element a a_1) False) % 86.70/86.90 (Or (Eq (prebool_difference a_1 a_2 a) (set_difference a_2 a)) % 86.70/86.90 (Or (Eq (And (Not (empty a_1)) (preboolean a_1)) False) (Eq (element a_2 a_1) False))) % 86.70/86.90 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 : Iota), % 86.70/86.90 Or (Eq (element a a_1) False) % 86.70/86.90 (Or (Eq (prebool_difference a_1 a_2 a) (set_difference a_2 a)) % 86.70/86.90 (Or (Eq (element a_2 a_1) False) (Or (Eq (Not (empty a_1)) False) (Eq (preboolean a_1) False)))) % 86.70/86.90 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 : Iota), % 86.70/86.90 Or (Eq (element a a_1) False) % 86.70/86.90 (Or (Eq (prebool_difference a_1 a_2 a) (set_difference a_2 a)) % 86.70/86.90 (Or (Eq (element a_2 a_1) False) (Or (Eq (preboolean a_1) False) (Eq (empty a_1) True)))) % 86.70/86.90 Clause #209 (by superposition #[206, 95]): ∀ (a a_1 a_2 : Iota), % 86.70/86.90 Or (Eq (prebool_difference a a_1 (skS.0 3 a a_2)) (set_difference a_1 (skS.0 3 a a_2))) % 86.70/86.90 (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Or (Eq (empty a) True) (Eq False True)))) % 86.70/86.90 Clause #219 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference a B) empty_set) (subset a B)) True % 86.70/86.90 Clause #220 (by clausification #[219]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference a a_1) empty_set) (subset a a_1)) True % 86.70/86.90 Clause #221 (by clausification #[220]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a a_1) empty_set) True) (Eq (subset a a_1) False) % 86.70/86.90 Clause #223 (by clausification #[221]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_difference a a_1) empty_set) % 86.70/86.90 Clause #225 (by superposition #[223, 49]): ∀ (a : Iota), Or (Eq (set_difference a a) empty_set) (Eq False True) % 86.70/86.90 Clause #226 (by clausification #[225]): ∀ (a : Iota), Eq (set_difference a a) empty_set % 86.70/86.90 Clause #252 (by clausification #[96]): ∀ (a a_1 a_2 : Iota), % 86.70/86.90 Or (Eq (element (prebool_difference a a_1 (skS.0 3 a a_2)) a) True) % 86.70/86.90 (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Eq (empty a) True))) % 86.76/86.96 Clause #255 (by superposition #[252, 95]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or (Eq (element (prebool_difference a (skS.0 3 a a_1) (skS.0 3 a a_2)) a) True) % 86.76/86.96 (Or (Eq (preboolean a) False) (Or (Eq (empty a) True) (Eq False True))) % 86.76/86.96 Clause #434 (by clausification #[209]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or (Eq (prebool_difference a a_1 (skS.0 3 a a_2)) (set_difference a_1 (skS.0 3 a a_2))) % 86.76/86.96 (Or (Eq (element a_1 a) False) (Or (Eq (preboolean a) False) (Eq (empty a) True))) % 86.76/86.96 Clause #439 (by superposition #[434, 95]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or (Eq (prebool_difference a (skS.0 3 a a_1) (skS.0 3 a a_2)) (set_difference (skS.0 3 a a_1) (skS.0 3 a a_2))) % 86.76/86.96 (Or (Eq (preboolean a) False) (Or (Eq (empty a) True) (Eq False True))) % 86.76/86.96 Clause #484 (by clausification #[255]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or (Eq (element (prebool_difference a (skS.0 3 a a_1) (skS.0 3 a a_2)) a) True) % 86.76/86.96 (Or (Eq (preboolean a) False) (Eq (empty a) True)) % 86.76/86.96 Clause #485 (by superposition #[484, 60]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or % 86.76/86.96 (Eq (element (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True) % 86.76/86.96 (Or (Eq (empty (skS.0 2 a)) True) (Eq False True)) % 86.76/86.96 Clause #932 (by clausification #[439]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or (Eq (prebool_difference a (skS.0 3 a a_1) (skS.0 3 a a_2)) (set_difference (skS.0 3 a a_1) (skS.0 3 a a_2))) % 86.76/86.96 (Or (Eq (preboolean a) False) (Eq (empty a) True)) % 86.76/86.96 Clause #933 (by superposition #[932, 60]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or % 86.76/86.96 (Eq (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) % 86.76/86.96 (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2))) % 86.76/86.96 (Or (Eq (empty (skS.0 2 a)) True) (Eq False True)) % 86.76/86.96 Clause #1166 (by clausification #[485]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or % 86.76/86.96 (Eq (element (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True) % 86.76/86.96 (Eq (empty (skS.0 2 a)) True) % 86.76/86.96 Clause #1167 (by forward demodulation #[1166, 111]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or % 86.76/86.96 (Eq (element (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True) % 86.76/86.96 (Eq False True) % 86.76/86.96 Clause #1168 (by clausification #[1167]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Eq (element (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True % 86.76/86.96 Clause #2338 (by clausification #[933]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or % 86.76/86.96 (Eq (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) % 86.76/86.96 (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2))) % 86.76/86.96 (Eq (empty (skS.0 2 a)) True) % 86.76/86.96 Clause #2339 (by forward demodulation #[2338, 111]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Or % 86.76/86.96 (Eq (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) % 86.76/86.96 (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2))) % 86.76/86.96 (Eq False True) % 86.76/86.96 Clause #2340 (by clausification #[2339]): ∀ (a a_1 a_2 : Iota), % 86.76/86.96 Eq (prebool_difference (skS.0 2 a) (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) % 86.76/86.96 (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) % 86.76/86.96 Clause #2341 (by backward demodulation #[2340, 1168]): ∀ (a a_1 a_2 : Iota), Eq (element (set_difference (skS.0 3 (skS.0 2 a) a_1) (skS.0 3 (skS.0 2 a) a_2)) (skS.0 2 a)) True % 86.76/86.96 Clause #3301 (by superposition #[2341, 226]): ∀ (a : Iota), Eq (element empty_set (skS.0 2 a)) True % 86.76/86.96 Clause #3303 (by superposition #[3301, 140]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (empty (skS.0 2 a)) True) (Eq (in empty_set (skS.0 2 a)) True)) % 86.76/86.96 Clause #3307 (by clausification #[3303]): ∀ (a : Iota), Or (Eq (empty (skS.0 2 a)) True) (Eq (in empty_set (skS.0 2 a)) True) % 86.76/86.96 Clause #3308 (by forward demodulation #[3307, 111]): ∀ (a : Iota), Or (Eq False True) (Eq (in empty_set (skS.0 2 a)) True) % 86.76/86.96 Clause #3309 (by clausification #[3308]): ∀ (a : Iota), Eq (in empty_set (skS.0 2 a)) True % 86.76/86.96 Clause #3310 (by superposition #[3309, 59]): Eq True False % 86.76/86.96 Clause #3316 (by clausification #[3310]): False % 86.76/86.96 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------