%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET903+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:00:39 PM UTC 2025 % Result : Theorem 5.61s 5.81s % Output : Proof 5.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET903+1 : TPTP v9.2.0. Released v3.2.0. % 0.10/0.11 % Command : duper %s % 0.11/0.32 % Computer : n005.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Thu Oct 2 14:01:08 EDT 2025 % 0.11/0.32 % CPUTime : % 5.61/5.81 SZS status Theorem for theBenchmark.p % 5.61/5.81 SZS output start Proof for theBenchmark.p % 5.61/5.81 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True % 5.61/5.81 Clause #7 (by assumption #[]): Eq % 5.61/5.81 (∀ (A B C : Iota), % 5.61/5.81 Not % 5.61/5.81 (And % 5.61/5.81 (And (And (Eq (singleton A) (set_union2 B C)) (Not (And (Eq B (singleton A)) (Eq C (singleton A))))) % 5.61/5.81 (Not (And (Eq B empty_set) (Eq C (singleton A))))) % 5.61/5.81 (Not (And (Eq B (singleton A)) (Eq C empty_set))))) % 5.61/5.81 True % 5.61/5.81 Clause #8 (by assumption #[]): Eq % 5.61/5.81 (Not % 5.61/5.81 (∀ (A B C : Iota), % 5.61/5.81 Not (And (And (And (Eq (singleton A) (set_union2 B C)) (Ne B C)) (Ne B empty_set)) (Ne C empty_set)))) % 5.61/5.81 True % 5.61/5.81 Clause #22 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True % 5.61/5.81 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True % 5.61/5.81 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a) % 5.61/5.81 Clause #30 (by clausification #[8]): Eq % 5.61/5.81 (∀ (A B C : Iota), % 5.61/5.81 Not (And (And (And (Eq (singleton A) (set_union2 B C)) (Ne B C)) (Ne B empty_set)) (Ne C empty_set))) % 5.61/5.81 False % 5.61/5.81 Clause #31 (by clausification #[30]): ∀ (a : Iota), % 5.61/5.81 Eq % 5.61/5.81 (Not % 5.61/5.81 (∀ (B C : Iota), % 5.61/5.81 Not (And (And (And (Eq (singleton (skS.0 2 a)) (set_union2 B C)) (Ne B C)) (Ne B empty_set)) (Ne C empty_set)))) % 5.61/5.81 True % 5.61/5.81 Clause #32 (by clausification #[31]): ∀ (a : Iota), % 5.61/5.81 Eq % 5.61/5.81 (∀ (B C : Iota), % 5.61/5.81 Not (And (And (And (Eq (singleton (skS.0 2 a)) (set_union2 B C)) (Ne B C)) (Ne B empty_set)) (Ne C empty_set))) % 5.61/5.81 False % 5.61/5.81 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), % 5.61/5.81 Eq % 5.61/5.81 (Not % 5.61/5.81 (∀ (C : Iota), % 5.61/5.81 Not % 5.61/5.81 (And % 5.61/5.81 (And (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) C)) (Ne (skS.0 3 a a_1) C)) % 5.61/5.81 (Ne (skS.0 3 a a_1) empty_set)) % 5.61/5.81 (Ne C empty_set)))) % 5.61/5.81 True % 5.61/5.81 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 5.61/5.81 Eq % 5.61/5.81 (∀ (C : Iota), % 5.61/5.81 Not % 5.61/5.81 (And % 5.61/5.81 (And (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) C)) (Ne (skS.0 3 a a_1) C)) % 5.61/5.81 (Ne (skS.0 3 a a_1) empty_set)) % 5.61/5.81 (Ne C empty_set))) % 5.61/5.81 False % 5.61/5.81 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), % 5.61/5.81 Eq % 5.61/5.81 (Not % 5.61/5.81 (Not % 5.61/5.81 (And % 5.61/5.81 (And % 5.61/5.81 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.61/5.81 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.61/5.81 (Ne (skS.0 3 a a_1) empty_set)) % 5.61/5.81 (Ne (skS.0 4 a a_1 a_2) empty_set)))) % 5.61/5.81 True % 5.61/5.81 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 5.61/5.81 Eq % 5.61/5.81 (Not % 5.61/5.81 (And % 5.61/5.81 (And % 5.61/5.81 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.61/5.81 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.61/5.81 (Ne (skS.0 3 a a_1) empty_set)) % 5.61/5.81 (Ne (skS.0 4 a a_1 a_2) empty_set))) % 5.61/5.81 False % 5.61/5.81 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), % 5.61/5.81 Eq % 5.61/5.81 (And % 5.61/5.81 (And % 5.61/5.81 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.61/5.81 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.61/5.81 (Ne (skS.0 3 a a_1) empty_set)) % 5.61/5.81 (Ne (skS.0 4 a a_1 a_2) empty_set)) % 5.61/5.81 True % 5.61/5.81 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Eq (Ne (skS.0 4 a a_1 a_2) empty_set) True % 5.61/5.81 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 5.61/5.81 Eq % 5.61/5.81 (And % 5.61/5.81 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.61/5.81 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.61/5.81 (Ne (skS.0 3 a a_1) empty_set)) % 5.61/5.81 True % 5.61/5.81 Clause #40 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 4 a a_1 a_2) empty_set % 5.61/5.81 Clause #41 (by clausification #[7]): ∀ (a : Iota), % 5.61/5.81 Eq % 5.61/5.81 (∀ (B C : Iota), % 5.61/5.81 Not % 5.61/5.81 (And % 5.61/5.81 (And (And (Eq (singleton a) (set_union2 B C)) (Not (And (Eq B (singleton a)) (Eq C (singleton a))))) % 5.61/5.81 (Not (And (Eq B empty_set) (Eq C (singleton a))))) % 5.61/5.81 (Not (And (Eq B (singleton a)) (Eq C empty_set))))) % 5.61/5.81 True % 5.61/5.81 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 5.61/5.86 Eq % 5.61/5.86 (∀ (C : Iota), % 5.61/5.86 Not % 5.61/5.86 (And % 5.61/5.86 (And (And (Eq (singleton a) (set_union2 a_1 C)) (Not (And (Eq a_1 (singleton a)) (Eq C (singleton a))))) % 5.61/5.86 (Not (And (Eq a_1 empty_set) (Eq C (singleton a))))) % 5.61/5.86 (Not (And (Eq a_1 (singleton a)) (Eq C empty_set))))) % 5.61/5.86 True % 5.61/5.86 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Eq % 5.61/5.86 (Not % 5.61/5.86 (And % 5.61/5.86 (And (And (Eq (singleton a) (set_union2 a_1 a_2)) (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a))))) % 5.61/5.86 (Not (And (Eq a_1 empty_set) (Eq a_2 (singleton a))))) % 5.61/5.86 (Not (And (Eq a_1 (singleton a)) (Eq a_2 empty_set))))) % 5.61/5.86 True % 5.61/5.86 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Eq % 5.61/5.86 (And % 5.61/5.86 (And (And (Eq (singleton a) (set_union2 a_1 a_2)) (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a))))) % 5.61/5.86 (Not (And (Eq a_1 empty_set) (Eq a_2 (singleton a))))) % 5.61/5.86 (Not (And (Eq a_1 (singleton a)) (Eq a_2 empty_set)))) % 5.61/5.86 False % 5.61/5.86 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or % 5.61/5.86 (Eq % 5.61/5.86 (And (And (Eq (singleton a) (set_union2 a_1 a_2)) (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a))))) % 5.61/5.86 (Not (And (Eq a_1 empty_set) (Eq a_2 (singleton a))))) % 5.61/5.86 False) % 5.61/5.86 (Eq (Not (And (Eq a_1 (singleton a)) (Eq a_2 empty_set))) False) % 5.61/5.86 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Eq (Not (And (Eq a (singleton a_1)) (Eq a_2 empty_set))) False) % 5.61/5.86 (Or % 5.61/5.86 (Eq (And (Eq (singleton a_1) (set_union2 a a_2)) (Not (And (Eq a (singleton a_1)) (Eq a_2 (singleton a_1))))) % 5.61/5.86 False) % 5.61/5.86 (Eq (Not (And (Eq a empty_set) (Eq a_2 (singleton a_1)))) False)) % 5.61/5.86 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Eq (And (Eq (singleton a) (set_union2 a_1 a_2)) (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a))))) False) % 5.61/5.86 (Or (Eq (Not (And (Eq a_1 empty_set) (Eq a_2 (singleton a)))) False) % 5.61/5.86 (Eq (And (Eq a_1 (singleton a)) (Eq a_2 empty_set)) True)) % 5.61/5.86 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Eq (Not (And (Eq a empty_set) (Eq a_1 (singleton a_2)))) False) % 5.61/5.86 (Or (Eq (And (Eq a (singleton a_2)) (Eq a_1 empty_set)) True) % 5.61/5.86 (Or (Eq (Eq (singleton a_2) (set_union2 a a_1)) False) % 5.61/5.86 (Eq (Not (And (Eq a (singleton a_2)) (Eq a_1 (singleton a_2)))) False))) % 5.61/5.86 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Eq (And (Eq a (singleton a_1)) (Eq a_2 empty_set)) True) % 5.61/5.86 (Or (Eq (Eq (singleton a_1) (set_union2 a a_2)) False) % 5.61/5.86 (Or (Eq (Not (And (Eq a (singleton a_1)) (Eq a_2 (singleton a_1)))) False) % 5.61/5.86 (Eq (And (Eq a empty_set) (Eq a_2 (singleton a_1))) True))) % 5.61/5.86 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Eq (Eq (singleton a) (set_union2 a_1 a_2)) False) % 5.61/5.86 (Or (Eq (Not (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a)))) False) % 5.61/5.86 (Or (Eq (And (Eq a_1 empty_set) (Eq a_2 (singleton a))) True) (Eq (Eq a_2 empty_set) True))) % 5.61/5.86 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Eq (Not (And (Eq a (singleton a_1)) (Eq a_2 (singleton a_1)))) False) % 5.61/5.86 (Or (Eq (And (Eq a empty_set) (Eq a_2 (singleton a_1))) True) % 5.61/5.86 (Or (Eq (Eq a_2 empty_set) True) (Ne (singleton a_1) (set_union2 a a_2)))) % 5.61/5.86 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Eq (And (Eq a empty_set) (Eq a_1 (singleton a_2))) True) % 5.61/5.86 (Or (Eq (Eq a_1 empty_set) True) % 5.61/5.86 (Or (Ne (singleton a_2) (set_union2 a a_1)) (Eq (And (Eq a (singleton a_2)) (Eq a_1 (singleton a_2))) True))) % 5.61/5.86 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Eq (Eq a empty_set) True) % 5.61/5.86 (Or (Ne (singleton a_1) (set_union2 a_2 a)) % 5.61/5.86 (Or (Eq (And (Eq a_2 (singleton a_1)) (Eq a (singleton a_1))) True) (Eq (Eq a (singleton a_1)) True))) % 5.61/5.86 Clause #56 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Ne (singleton a) (set_union2 a_1 a_2)) % 5.61/5.86 (Or (Eq (And (Eq a_1 (singleton a)) (Eq a_2 (singleton a))) True) % 5.61/5.86 (Or (Eq (Eq a_2 (singleton a)) True) (Eq a_2 empty_set))) % 5.61/5.86 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 5.61/5.86 Or (Ne (singleton a) (set_union2 a_1 a_2)) % 5.70/5.90 (Or (Eq (Eq a_2 (singleton a)) True) (Or (Eq a_2 empty_set) (Eq (Eq a_2 (singleton a)) True))) % 5.70/5.90 Clause #59 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 5.70/5.90 Or (Ne (singleton a) (set_union2 a_1 a_2)) % 5.70/5.90 (Or (Eq a_2 empty_set) (Or (Eq (Eq a_2 (singleton a)) True) (Eq a_2 (singleton a)))) % 5.70/5.90 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 : Iota), % 5.70/5.90 Or (Ne (singleton a) (set_union2 a_1 a_2)) (Or (Eq a_2 empty_set) (Or (Eq a_2 (singleton a)) (Eq a_2 (singleton a)))) % 5.70/5.90 Clause #61 (by eliminate duplicate literals #[60]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (set_union2 a_1 a_2)) (Or (Eq a_2 empty_set) (Eq a_2 (singleton a))) % 5.70/5.90 Clause #63 (by superposition #[61, 24]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (set_union2 a_1 a_2)) (Or (Eq a_1 empty_set) (Eq a_1 (singleton a))) % 5.70/5.90 Clause #64 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 3 a a_1) empty_set) True % 5.70/5.90 Clause #65 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 5.70/5.90 Eq % 5.70/5.90 (And (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.70/5.90 (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) % 5.70/5.90 True % 5.70/5.90 Clause #66 (by clausification #[64]): ∀ (a a_1 : Iota), Ne (skS.0 3 a a_1) empty_set % 5.70/5.90 Clause #98 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Eq (Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True % 5.70/5.90 Clause #99 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Eq (Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) True % 5.70/5.90 Clause #100 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 3 a a_1) (skS.0 4 a a_1 a_2) % 5.70/5.90 Clause #101 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), Eq (singleton (skS.0 2 a)) (set_union2 (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) % 5.70/5.90 Clause #104 (by superposition #[101, 61]): ∀ (a a_1 a_2 a_3 : Iota), % 5.70/5.90 Or (Ne (singleton a) (singleton (skS.0 2 a_1))) % 5.70/5.90 (Or (Eq (skS.0 4 a_1 a_2 a_3) empty_set) (Eq (skS.0 4 a_1 a_2 a_3) (singleton a))) % 5.70/5.90 Clause #105 (by superposition #[101, 63]): ∀ (a a_1 a_2 : Iota), % 5.70/5.90 Or (Ne (singleton a) (singleton (skS.0 2 a_1))) % 5.70/5.90 (Or (Eq (skS.0 3 a_1 a_2) empty_set) (Eq (skS.0 3 a_1 a_2) (singleton a))) % 5.70/5.90 Clause #106 (by forward contextual literal cutting #[105, 66]): ∀ (a a_1 a_2 : Iota), Or (Ne (singleton a) (singleton (skS.0 2 a_1))) (Eq (skS.0 3 a_1 a_2) (singleton a)) % 5.70/5.90 Clause #107 (by equality resolution #[106]): ∀ (a a_1 : Iota), Eq (skS.0 3 a a_1) (singleton (skS.0 2 a)) % 5.70/5.90 Clause #109 (by backward demodulation #[107, 100]): ∀ (a a_1 a_2 : Iota), Ne (singleton (skS.0 2 a)) (skS.0 4 a a_1 a_2) % 5.70/5.90 Clause #113 (by forward contextual literal cutting #[104, 40]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne (singleton a) (singleton (skS.0 2 a_1))) (Eq (skS.0 4 a_1 a_2 a_3) (singleton a)) % 5.70/5.90 Clause #114 (by equality resolution #[113]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 4 a a_1 a_2) (singleton (skS.0 2 a)) % 5.70/5.90 Clause #115 (by forward contextual literal cutting #[114, 109]): False % 5.70/5.90 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------