%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU572^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:01:56 PM UTC 2025 % Result : Theorem 3.76s 3.93s % Output : Proof 3.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU572^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n008.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 04:51:53 EDT 2025 % 0.12/0.34 % CPUTime : % 3.76/3.93 SZS status Theorem for theBenchmark.p % 3.76/3.93 SZS output start Proof for theBenchmark.p % 3.76/3.93 Clause #0 (by assumption #[]): Eq (Eq subsetTrans (∀ (A B C : Iota), subset A B → subset B C → subset A C)) True % 3.76/3.93 Clause #1 (by assumption #[]): Eq (Eq setadjoinSub (∀ (Xx A : Iota), subset A (setadjoin Xx A))) True % 3.76/3.93 Clause #2 (by assumption #[]): Eq (Not (subsetTrans → setadjoinSub → ∀ (A Xx B : Iota), subset A B → subset A (setadjoin Xx B))) True % 3.76/3.93 Clause #3 (by clausification #[1]): Eq setadjoinSub (∀ (Xx A : Iota), subset A (setadjoin Xx A)) % 3.76/3.93 Clause #5 (by clausify Prop equality #[3]): Or (Eq setadjoinSub False) (Eq (∀ (Xx A : Iota), subset A (setadjoin Xx A)) True) % 3.76/3.93 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq setadjoinSub False) (Eq (∀ (A : Iota), subset A (setadjoin a A)) True) % 3.76/3.93 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq setadjoinSub False) (Eq (subset a (setadjoin a_1 a)) True) % 3.76/3.93 Clause #13 (by clausification #[0]): Eq subsetTrans (∀ (A B C : Iota), subset A B → subset B C → subset A C) % 3.76/3.93 Clause #17 (by clausification #[2]): Eq (subsetTrans → setadjoinSub → ∀ (A Xx B : Iota), subset A B → subset A (setadjoin Xx B)) False % 3.76/3.93 Clause #18 (by clausification #[17]): Eq subsetTrans True % 3.76/3.93 Clause #19 (by clausification #[17]): Eq (setadjoinSub → ∀ (A Xx B : Iota), subset A B → subset A (setadjoin Xx B)) False % 3.76/3.93 Clause #20 (by backward demodulation #[18, 13]): Eq True (∀ (A B C : Iota), subset A B → subset B C → subset A C) % 3.76/3.93 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B C : Iota), subset a B → subset B C → subset a C) True % 3.76/3.93 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), subset a a_1 → subset a_1 C → subset a C) True % 3.76/3.93 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → subset a_1 a_2 → subset a a_2) True % 3.76/3.93 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (subset a_1 a_2 → subset a a_2) True) % 3.76/3.93 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (subset a_1 a_2) False) (Eq (subset a a_2) True)) % 3.76/3.93 Clause #26 (by clausification #[19]): Eq setadjoinSub True % 3.76/3.93 Clause #27 (by clausification #[19]): Eq (∀ (A Xx B : Iota), subset A B → subset A (setadjoin Xx B)) False % 3.76/3.93 Clause #29 (by backward demodulation #[26, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (subset a (setadjoin a_1 a)) True) % 3.76/3.93 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (subset a (setadjoin a_1 a)) True % 3.76/3.93 Clause #34 (by clausification #[27]): ∀ (a : Iota), Eq (Not (∀ (Xx B : Iota), subset (skS.0 2 a) B → subset (skS.0 2 a) (setadjoin Xx B))) True % 3.76/3.93 Clause #35 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (Xx B : Iota), subset (skS.0 2 a) B → subset (skS.0 2 a) (setadjoin Xx B)) False % 3.76/3.93 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Not (∀ (B : Iota), subset (skS.0 2 a) B → subset (skS.0 2 a) (setadjoin (skS.0 3 a a_1) B))) True % 3.76/3.93 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (∀ (B : Iota), subset (skS.0 2 a) B → subset (skS.0 2 a) (setadjoin (skS.0 3 a a_1) B)) False % 3.76/3.93 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 3.76/3.93 Eq (Not (subset (skS.0 2 a) (skS.0 4 a a_1 a_2) → subset (skS.0 2 a) (setadjoin (skS.0 3 a a_1) (skS.0 4 a a_1 a_2)))) % 3.76/3.93 True % 3.76/3.93 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 3.76/3.93 Eq (subset (skS.0 2 a) (skS.0 4 a a_1 a_2) → subset (skS.0 2 a) (setadjoin (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) False % 3.76/3.93 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 2 a) (skS.0 4 a a_1 a_2)) True % 3.76/3.93 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 2 a) (setadjoin (skS.0 3 a a_1) (skS.0 4 a a_1 a_2))) False % 3.76/3.93 Clause #42 (by superposition #[40, 25]): ∀ (a a_1 a_2 a_3 : Iota), % 3.76/3.93 Or (Eq True False) (Or (Eq (subset (skS.0 4 a a_1 a_2) a_3) False) (Eq (subset (skS.0 2 a) a_3) True)) % 3.76/3.93 Clause #88 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (subset (skS.0 4 a a_1 a_2) a_3) False) (Eq (subset (skS.0 2 a) a_3) True) % 3.76/3.93 Clause #89 (by superposition #[88, 31]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (subset (skS.0 2 a) (setadjoin a_1 (skS.0 4 a a_2 a_3))) True) (Eq False True) % 3.76/3.93 Clause #112 (by clausification #[89]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 2 a) (setadjoin a_1 (skS.0 4 a a_2 a_3))) True % 3.76/3.93 Clause #113 (by superposition #[112, 41]): Eq True False % 3.76/3.93 Clause #115 (by clausification #[113]): False % 3.76/3.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------