%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET929+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:00:43 PM UTC 2025 % Result : Theorem 4.56s 4.79s % Output : Proof 4.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SET929+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.14 % Command : duper %s % 0.12/0.35 % Computer : n019.cluster.edu % 0.12/0.35 % Model : x86_64 x86_64 % 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.35 % Memory : 8042.1875MB % 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.35 % CPULimit : 300 % 0.12/0.35 % WCLimit : 300 % 0.12/0.35 % DateTime : Thu Oct 2 13:56:08 EDT 2025 % 0.12/0.35 % CPUTime : % 4.56/4.79 SZS status Theorem for theBenchmark.p % 4.56/4.79 SZS output start Proof for theBenchmark.p % 4.56/4.79 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 4.56/4.79 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference A B) empty_set) (subset A B)) True % 4.56/4.79 Clause #7 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (subset (unordered_pair A B) C) (And (in A C) (in B C))) True % 4.56/4.79 Clause #8 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Iff (Eq (set_difference (unordered_pair A B) C) empty_set) (And (in A C) (in B C)))) True % 4.56/4.79 Clause #19 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 4.56/4.79 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 4.56/4.79 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 4.56/4.79 Clause #22 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference a B) empty_set) (subset a B)) True % 4.56/4.79 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference a a_1) empty_set) (subset a a_1)) True % 4.56/4.79 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a a_1) empty_set) True) (Eq (subset a a_1) False) % 4.56/4.79 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference a a_1) empty_set) False) (Eq (subset a a_1) True) % 4.56/4.79 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (set_difference a a_1) empty_set) % 4.56/4.79 Clause #29 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Ne (set_difference a a_1) empty_set) % 4.56/4.79 Clause #32 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (subset (unordered_pair a B) C) (And (in a C) (in B C))) True % 4.56/4.79 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Iff (subset (unordered_pair a a_1) C) (And (in a C) (in a_1 C))) True % 4.56/4.79 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (Iff (subset (unordered_pair a a_1) a_2) (And (in a a_2) (in a_1 a_2))) True % 4.56/4.79 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) True) (Eq (And (in a a_2) (in a_1 a_2)) False) % 4.56/4.79 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) False) (Eq (And (in a a_2) (in a_1 a_2)) True) % 4.56/4.79 Clause #37 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), % 4.56/4.79 Or (Eq (subset (unordered_pair a a_1) a_2) True) (Or (Eq (in a a_2) False) (Eq (in a_1 a_2) False)) % 4.56/4.79 Clause #38 (by clausification #[8]): Eq (∀ (A B C : Iota), Iff (Eq (set_difference (unordered_pair A B) C) empty_set) (And (in A C) (in B C))) False % 4.56/4.79 Clause #39 (by clausification #[38]): ∀ (a : Iota), % 4.56/4.79 Eq % 4.56/4.79 (Not % 4.56/4.79 (∀ (B C : Iota), % 4.56/4.79 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) B) C) empty_set) (And (in (skS.0 2 a) C) (in B C)))) % 4.56/4.79 True % 4.56/4.79 Clause #40 (by clausification #[39]): ∀ (a : Iota), % 4.56/4.79 Eq % 4.56/4.79 (∀ (B C : Iota), % 4.56/4.79 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) B) C) empty_set) (And (in (skS.0 2 a) C) (in B C))) % 4.56/4.79 False % 4.56/4.79 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 4.56/4.79 Eq % 4.56/4.79 (Not % 4.56/4.79 (∀ (C : Iota), % 4.56/4.79 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) empty_set) % 4.56/4.79 (And (in (skS.0 2 a) C) (in (skS.0 3 a a_1) C)))) % 4.56/4.79 True % 4.56/4.79 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 4.56/4.79 Eq % 4.56/4.79 (∀ (C : Iota), % 4.56/4.79 Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) C) empty_set) % 4.56/4.79 (And (in (skS.0 2 a) C) (in (skS.0 3 a a_1) C))) % 4.56/4.79 False % 4.56/4.79 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 4.56/4.79 Eq % 4.56/4.79 (Not % 4.56/4.79 (Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.56/4.79 (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))))) % 4.56/4.79 True % 4.56/4.79 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 4.56/4.79 Eq % 4.56/4.79 (Iff (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.62/4.82 (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))) % 4.62/4.82 False % 4.62/4.82 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) False) % 4.62/4.82 (Eq (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) False) % 4.62/4.82 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) True) % 4.62/4.82 (Eq (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) True) % 4.62/4.82 Clause #47 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) False) % 4.62/4.82 (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.62/4.82 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.62/4.82 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) False)) % 4.62/4.82 Clause #49 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) False) (Eq (in a_1 a_2) True) % 4.62/4.82 Clause #50 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (unordered_pair a a_1) a_2) False) (Eq (in a a_2) True) % 4.62/4.82 Clause #60 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (And (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) True) % 4.62/4.82 (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.62/4.82 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.62/4.82 (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) % 4.62/4.82 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.62/4.82 (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 4.62/4.82 Clause #64 (by superposition #[61, 29]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) % 4.62/4.82 (Or (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True) (Ne empty_set empty_set)) % 4.62/4.82 Clause #82 (by superposition #[62, 29]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 4.62/4.82 (Or (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True) (Ne empty_set empty_set)) % 4.62/4.82 Clause #90 (by eliminate resolved literals #[64]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) % 4.62/4.82 (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True) % 4.62/4.82 Clause #91 (by superposition #[90, 49]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) % 4.62/4.82 (Or (Eq True False) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True)) % 4.62/4.82 Clause #98 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) (Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True) % 4.62/4.82 Clause #99 (by eliminate duplicate literals #[98]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)) True % 4.62/4.82 Clause #100 (by backward demodulation #[99, 48]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.62/4.82 (Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False) (Eq True False)) % 4.62/4.82 Clause #104 (by superposition #[99, 37]): ∀ (a a_1 a_2 a_3 : Iota), % 4.62/4.82 Or (Eq (subset (unordered_pair (skS.0 3 a a_1) a_2) (skS.0 4 a a_1 a_3)) True) % 4.62/4.82 (Or (Eq True False) (Eq (in a_2 (skS.0 4 a a_1 a_3)) False)) % 4.62/4.82 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), % 4.62/4.82 Or (Eq (subset (unordered_pair (skS.0 3 a a_1) a_2) (skS.0 4 a a_1 a_3)) True) (Eq (in a_2 (skS.0 4 a a_1 a_3)) False) % 4.62/4.82 Clause #113 (by eliminate resolved literals #[82]): ∀ (a a_1 a_2 : Iota), % 4.62/4.82 Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 4.62/4.83 (Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True) % 4.62/4.83 Clause #115 (by superposition #[113, 50]): ∀ (a a_1 a_2 : Iota), % 4.62/4.83 Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Or (Eq True False) (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True)) % 4.62/4.83 Clause #117 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True) % 4.62/4.83 Clause #118 (by eliminate duplicate literals #[117]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 4.62/4.83 Clause #119 (by superposition #[118, 106]): ∀ (a a_1 a_2 : Iota), % 4.62/4.83 Or (Eq (subset (unordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (skS.0 4 a a_1 a_2)) True) (Eq True False) % 4.62/4.83 Clause #123 (by clausification #[119]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 3 a a_1) (skS.0 2 a)) (skS.0 4 a a_1 a_2)) True % 4.62/4.83 Clause #124 (by forward demodulation #[123, 21]): ∀ (a a_1 a_2 : Iota), Eq (subset (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) True % 4.62/4.83 Clause #126 (by superposition #[124, 26]): ∀ (a a_1 a_2 : Iota), % 4.62/4.83 Or (Eq True False) (Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.62/4.83 Clause #129 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), Eq (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set % 4.62/4.83 Clause #143 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), % 4.62/4.83 Or (Ne (set_difference (unordered_pair (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 4 a a_1 a_2)) empty_set) % 4.62/4.83 (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False) % 4.62/4.83 Clause #144 (by forward demodulation #[143, 129]): ∀ (a a_1 a_2 : Iota), Or (Ne empty_set empty_set) (Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False) % 4.62/4.83 Clause #145 (by eliminate resolved literals #[144]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 a) (skS.0 4 a a_1 a_2)) False % 4.62/4.83 Clause #146 (by superposition #[145, 118]): Eq False True % 4.62/4.83 Clause #147 (by clausification #[146]): False % 4.62/4.83 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------