%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LAT382+3 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 07:53:33 PM UTC 2025 % Result : Theorem 20.05s 20.23s % Output : Proof 20.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : LAT382+3 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n021.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 : Thu Oct 2 18:34:08 EDT 2025 % 0.12/0.34 % CPUTime : % 20.05/20.23 SZS status Theorem for theBenchmark.p % 20.05/20.23 SZS output start Proof for theBenchmark.p % 20.05/20.23 Clause #2 (by assumption #[]): Eq (∀ (W0 : Iota), aSet0 W0 → ∀ (W1 : Iota), aElementOf0 W1 W0 → aElement0 W1) True % 20.05/20.23 Clause #7 (by assumption #[]): Eq (∀ (W0 W1 : Iota), And (aElement0 W0) (aElement0 W1) → And (sdtlseqdt0 W0 W1) (sdtlseqdt0 W1 W0) → Eq W0 W1) True % 20.05/20.23 Clause #9 (by assumption #[]): Eq % 20.05/20.23 (∀ (W0 : Iota), % 20.05/20.23 aSet0 W0 → % 20.05/20.23 ∀ (W1 : Iota), % 20.05/20.23 aSubsetOf0 W1 W0 → % 20.05/20.23 ∀ (W2 : Iota), % 20.05/20.23 Iff (aLowerBoundOfIn0 W2 W1 W0) % 20.05/20.23 (And (aElementOf0 W2 W0) (∀ (W3 : Iota), aElementOf0 W3 W1 → sdtlseqdt0 W2 W3))) % 20.05/20.23 True % 20.05/20.23 Clause #11 (by assumption #[]): Eq % 20.05/20.23 (∀ (W0 : Iota), % 20.05/20.23 aSet0 W0 → % 20.05/20.23 ∀ (W1 : Iota), % 20.05/20.23 aSubsetOf0 W1 W0 → % 20.05/20.23 ∀ (W2 : Iota), % 20.05/20.23 Iff (aInfimumOfIn0 W2 W1 W0) % 20.05/20.23 (And (And (aElementOf0 W2 W0) (aLowerBoundOfIn0 W2 W1 W0)) % 20.05/20.23 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 W1 W0 → sdtlseqdt0 W3 W2))) % 20.05/20.23 True % 20.05/20.23 Clause #14 (by assumption #[]): Eq (aSet0 xT) True % 20.05/20.23 Clause #15 (by assumption #[]): Eq (And (And (aSet0 xS) (∀ (W0 : Iota), aElementOf0 W0 xS → aElementOf0 W0 xT)) (aSubsetOf0 xS xT)) True % 20.05/20.23 Clause #16 (by assumption #[]): Eq % 20.05/20.23 (And % 20.05/20.23 (And % 20.05/20.23 (And % 20.05/20.23 (And % 20.05/20.23 (And % 20.05/20.23 (And % 20.05/20.23 (And % 20.05/20.23 (And % 20.05/20.23 (And % 20.05/20.23 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) % 20.05/20.23 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0)) % 20.05/20.23 (aLowerBoundOfIn0 xu xS xT)) % 20.05/20.23 (∀ (W0 : Iota), % 20.05/20.23 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) % 20.05/20.23 (aLowerBoundOfIn0 W0 xS xT) → % 20.05/20.23 sdtlseqdt0 W0 xu)) % 20.05/20.23 (aInfimumOfIn0 xu xS xT)) % 20.05/20.23 (aElementOf0 xv xT)) % 20.05/20.23 (aElementOf0 xv xT)) % 20.05/20.23 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xv W0)) % 20.05/20.23 (aLowerBoundOfIn0 xv xS xT)) % 20.05/20.23 (∀ (W0 : Iota), % 20.05/20.23 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) (aLowerBoundOfIn0 W0 xS xT) → % 20.05/20.23 sdtlseqdt0 W0 xv)) % 20.05/20.23 (aInfimumOfIn0 xv xS xT)) % 20.05/20.23 True % 20.05/20.23 Clause #17 (by assumption #[]): Eq (Not (Eq xu xv)) True % 20.05/20.23 Clause #29 (by clausification #[2]): ∀ (a : Iota), Eq (aSet0 a → ∀ (W1 : Iota), aElementOf0 W1 a → aElement0 W1) True % 20.05/20.23 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (aSet0 a) False) (Eq (∀ (W1 : Iota), aElementOf0 W1 a → aElement0 W1) True) % 20.05/20.23 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (aSet0 a) False) (Eq (aElementOf0 a_1 a → aElement0 a_1) True) % 20.05/20.23 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (aSet0 a) False) (Or (Eq (aElementOf0 a_1 a) False) (Eq (aElement0 a_1) True)) % 20.05/20.23 Clause #33 (by superposition #[32, 14]): ∀ (a : Iota), Or (Eq (aElementOf0 a xT) False) (Or (Eq (aElement0 a) True) (Eq False True)) % 20.05/20.23 Clause #34 (by clausification #[17]): Eq (Eq xu xv) False % 20.05/20.23 Clause #35 (by clausification #[34]): Ne xu xv % 20.05/20.23 Clause #36 (by clausification #[7]): ∀ (a : Iota), % 20.05/20.23 Eq (∀ (W1 : Iota), And (aElement0 a) (aElement0 W1) → And (sdtlseqdt0 a W1) (sdtlseqdt0 W1 a) → Eq a W1) True % 20.05/20.23 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (And (aElement0 a) (aElement0 a_1) → And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a) → Eq a a_1) True % 20.05/20.23 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 20.05/20.23 Or (Eq (And (aElement0 a) (aElement0 a_1)) False) (Eq (And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a) → Eq a a_1) True) % 20.05/20.23 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 20.05/20.23 Or (Eq (And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a) → Eq a a_1) True) % 20.05/20.23 (Or (Eq (aElement0 a) False) (Eq (aElement0 a_1) False)) % 20.05/20.23 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 20.05/20.23 Or (Eq (aElement0 a) False) % 20.05/20.23 (Or (Eq (aElement0 a_1) False) (Or (Eq (And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a)) False) (Eq (Eq a a_1) True))) % 20.05/20.23 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 20.05/20.23 Or (Eq (aElement0 a) False) % 20.05/20.23 (Or (Eq (aElement0 a_1) False) % 20.08/20.25 (Or (Eq (Eq a a_1) True) (Or (Eq (sdtlseqdt0 a a_1) False) (Eq (sdtlseqdt0 a_1 a) False)))) % 20.08/20.25 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 20.08/20.25 Or (Eq (aElement0 a) False) % 20.08/20.25 (Or (Eq (aElement0 a_1) False) (Or (Eq (sdtlseqdt0 a a_1) False) (Or (Eq (sdtlseqdt0 a_1 a) False) (Eq a a_1)))) % 20.08/20.25 Clause #51 (by clausification #[33]): ∀ (a : Iota), Or (Eq (aElementOf0 a xT) False) (Eq (aElement0 a) True) % 20.08/20.25 Clause #69 (by clausification #[15]): Eq (aSubsetOf0 xS xT) True % 20.08/20.25 Clause #106 (by clausification #[9]): ∀ (a : Iota), % 20.08/20.25 Eq % 20.08/20.25 (aSet0 a → % 20.08/20.25 ∀ (W1 : Iota), % 20.08/20.25 aSubsetOf0 W1 a → % 20.08/20.25 ∀ (W2 : Iota), % 20.08/20.25 Iff (aLowerBoundOfIn0 W2 W1 a) % 20.08/20.25 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 W1 → sdtlseqdt0 W2 W3))) % 20.08/20.25 True % 20.08/20.25 Clause #107 (by clausification #[106]): ∀ (a : Iota), % 20.08/20.25 Or (Eq (aSet0 a) False) % 20.08/20.25 (Eq % 20.08/20.25 (∀ (W1 : Iota), % 20.08/20.25 aSubsetOf0 W1 a → % 20.08/20.25 ∀ (W2 : Iota), % 20.08/20.25 Iff (aLowerBoundOfIn0 W2 W1 a) % 20.08/20.25 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 W1 → sdtlseqdt0 W2 W3))) % 20.08/20.25 True) % 20.08/20.25 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota), % 20.08/20.25 Or (Eq (aSet0 a) False) % 20.08/20.25 (Eq % 20.08/20.25 (aSubsetOf0 a_1 a → % 20.08/20.25 ∀ (W2 : Iota), % 20.08/20.25 Iff (aLowerBoundOfIn0 W2 a_1 a) % 20.08/20.25 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 W2 W3))) % 20.08/20.25 True) % 20.08/20.25 Clause #109 (by clausification #[108]): ∀ (a a_1 : Iota), % 20.08/20.25 Or (Eq (aSet0 a) False) % 20.08/20.25 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.25 (Eq % 20.08/20.25 (∀ (W2 : Iota), % 20.08/20.25 Iff (aLowerBoundOfIn0 W2 a_1 a) % 20.08/20.25 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 W2 W3))) % 20.08/20.25 True)) % 20.08/20.25 Clause #110 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), % 20.08/20.25 Or (Eq (aSet0 a) False) % 20.08/20.25 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.25 (Eq % 20.08/20.25 (Iff (aLowerBoundOfIn0 a_2 a_1 a) % 20.08/20.25 (And (aElementOf0 a_2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 a_2 W3))) % 20.08/20.25 True)) % 20.08/20.25 Clause #112 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), % 20.08/20.25 Or (Eq (aSet0 a) False) % 20.08/20.25 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.25 (Or (Eq (aLowerBoundOfIn0 a_2 a_1 a) False) % 20.08/20.25 (Eq (And (aElementOf0 a_2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 a_2 W3)) True))) % 20.08/20.25 Clause #153 (by clausification #[11]): ∀ (a : Iota), % 20.08/20.25 Eq % 20.08/20.25 (aSet0 a → % 20.08/20.25 ∀ (W1 : Iota), % 20.08/20.25 aSubsetOf0 W1 a → % 20.08/20.25 ∀ (W2 : Iota), % 20.08/20.25 Iff (aInfimumOfIn0 W2 W1 a) % 20.08/20.25 (And (And (aElementOf0 W2 a) (aLowerBoundOfIn0 W2 W1 a)) % 20.08/20.25 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 W1 a → sdtlseqdt0 W3 W2))) % 20.08/20.25 True % 20.08/20.25 Clause #154 (by clausification #[153]): ∀ (a : Iota), % 20.08/20.25 Or (Eq (aSet0 a) False) % 20.08/20.25 (Eq % 20.08/20.25 (∀ (W1 : Iota), % 20.08/20.25 aSubsetOf0 W1 a → % 20.08/20.25 ∀ (W2 : Iota), % 20.08/20.25 Iff (aInfimumOfIn0 W2 W1 a) % 20.08/20.25 (And (And (aElementOf0 W2 a) (aLowerBoundOfIn0 W2 W1 a)) % 20.08/20.25 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 W1 a → sdtlseqdt0 W3 W2))) % 20.08/20.25 True) % 20.08/20.25 Clause #155 (by clausification #[154]): ∀ (a a_1 : Iota), % 20.08/20.25 Or (Eq (aSet0 a) False) % 20.08/20.25 (Eq % 20.08/20.25 (aSubsetOf0 a_1 a → % 20.08/20.25 ∀ (W2 : Iota), % 20.08/20.25 Iff (aInfimumOfIn0 W2 a_1 a) % 20.08/20.25 (And (And (aElementOf0 W2 a) (aLowerBoundOfIn0 W2 a_1 a)) % 20.08/20.25 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 W2))) % 20.08/20.25 True) % 20.08/20.25 Clause #156 (by clausification #[155]): ∀ (a a_1 : Iota), % 20.08/20.25 Or (Eq (aSet0 a) False) % 20.08/20.25 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.25 (Eq % 20.08/20.25 (∀ (W2 : Iota), % 20.08/20.25 Iff (aInfimumOfIn0 W2 a_1 a) % 20.08/20.25 (And (And (aElementOf0 W2 a) (aLowerBoundOfIn0 W2 a_1 a)) % 20.08/20.25 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 W2))) % 20.08/20.25 True)) % 20.08/20.25 Clause #157 (by clausification #[156]): ∀ (a a_1 a_2 : Iota), % 20.08/20.25 Or (Eq (aSet0 a) False) % 20.08/20.25 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.25 (Eq % 20.08/20.25 (Iff (aInfimumOfIn0 a_2 a_1 a) % 20.08/20.25 (And (And (aElementOf0 a_2 a) (aLowerBoundOfIn0 a_2 a_1 a)) % 20.08/20.25 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 a_2))) % 20.08/20.25 True)) % 20.08/20.27 Clause #159 (by clausification #[157]): ∀ (a a_1 a_2 : Iota), % 20.08/20.27 Or (Eq (aSet0 a) False) % 20.08/20.27 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.27 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) % 20.08/20.27 (Eq % 20.08/20.27 (And (And (aElementOf0 a_2 a) (aLowerBoundOfIn0 a_2 a_1 a)) % 20.08/20.27 (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 a_2)) % 20.08/20.27 True))) % 20.08/20.27 Clause #208 (by clausification #[16]): Eq (aInfimumOfIn0 xv xS xT) True % 20.08/20.27 Clause #209 (by clausification #[16]): Eq % 20.08/20.27 (And % 20.08/20.27 (And % 20.08/20.27 (And % 20.08/20.27 (And % 20.08/20.27 (And % 20.08/20.27 (And % 20.08/20.27 (And % 20.08/20.27 (And % 20.08/20.27 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) % 20.08/20.27 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0)) % 20.08/20.27 (aLowerBoundOfIn0 xu xS xT)) % 20.08/20.27 (∀ (W0 : Iota), % 20.08/20.27 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) % 20.08/20.27 (aLowerBoundOfIn0 W0 xS xT) → % 20.08/20.27 sdtlseqdt0 W0 xu)) % 20.08/20.27 (aInfimumOfIn0 xu xS xT)) % 20.08/20.27 (aElementOf0 xv xT)) % 20.08/20.27 (aElementOf0 xv xT)) % 20.08/20.27 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xv W0)) % 20.08/20.27 (aLowerBoundOfIn0 xv xS xT)) % 20.08/20.27 (∀ (W0 : Iota), % 20.08/20.27 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) (aLowerBoundOfIn0 W0 xS xT) → % 20.08/20.27 sdtlseqdt0 W0 xv)) % 20.08/20.27 True % 20.08/20.27 Clause #218 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), % 20.08/20.27 Or (Eq (aSet0 a) False) % 20.08/20.27 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aLowerBoundOfIn0 a_2 a_1 a) False) (Eq (aElementOf0 a_2 a) True))) % 20.08/20.27 Clause #223 (by superposition #[218, 14]): ∀ (a a_1 : Iota), % 20.08/20.27 Or (Eq (aSubsetOf0 a xT) False) % 20.08/20.27 (Or (Eq (aLowerBoundOfIn0 a_1 a xT) False) (Or (Eq (aElementOf0 a_1 xT) True) (Eq False True))) % 20.08/20.27 Clause #228 (by clausification #[223]): ∀ (a a_1 : Iota), % 20.08/20.27 Or (Eq (aSubsetOf0 a xT) False) (Or (Eq (aLowerBoundOfIn0 a_1 a xT) False) (Eq (aElementOf0 a_1 xT) True)) % 20.08/20.27 Clause #229 (by superposition #[228, 69]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Or (Eq (aElementOf0 a xT) True) (Eq False True)) % 20.08/20.27 Clause #230 (by clausification #[229]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Eq (aElementOf0 a xT) True) % 20.08/20.27 Clause #383 (by clausification #[159]): ∀ (a a_1 a_2 : Iota), % 20.08/20.27 Or (Eq (aSet0 a) False) % 20.08/20.27 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.27 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) % 20.08/20.27 (Eq (∀ (W3 : Iota), aLowerBoundOfIn0 W3 a_1 a → sdtlseqdt0 W3 a_2) True))) % 20.08/20.27 Clause #384 (by clausification #[159]): ∀ (a a_1 a_2 : Iota), % 20.08/20.27 Or (Eq (aSet0 a) False) % 20.08/20.27 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.27 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) (Eq (And (aElementOf0 a_2 a) (aLowerBoundOfIn0 a_2 a_1 a)) True))) % 20.08/20.27 Clause #385 (by clausification #[383]): ∀ (a a_1 a_2 a_3 : Iota), % 20.08/20.27 Or (Eq (aSet0 a) False) % 20.08/20.27 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.27 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) (Eq (aLowerBoundOfIn0 a_3 a_1 a → sdtlseqdt0 a_3 a_2) True))) % 20.08/20.27 Clause #386 (by clausification #[385]): ∀ (a a_1 a_2 a_3 : Iota), % 20.08/20.27 Or (Eq (aSet0 a) False) % 20.08/20.27 (Or (Eq (aSubsetOf0 a_1 a) False) % 20.08/20.27 (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) % 20.08/20.27 (Or (Eq (aLowerBoundOfIn0 a_3 a_1 a) False) (Eq (sdtlseqdt0 a_3 a_2) True)))) % 20.08/20.27 Clause #387 (by superposition #[386, 14]): ∀ (a a_1 a_2 : Iota), % 20.08/20.27 Or (Eq (aSubsetOf0 a xT) False) % 20.08/20.27 (Or (Eq (aInfimumOfIn0 a_1 a xT) False) % 20.08/20.27 (Or (Eq (aLowerBoundOfIn0 a_2 a xT) False) (Or (Eq (sdtlseqdt0 a_2 a_1) True) (Eq False True)))) % 20.08/20.27 Clause #392 (by clausification #[387]): ∀ (a a_1 a_2 : Iota), % 20.08/20.27 Or (Eq (aSubsetOf0 a xT) False) % 20.08/20.27 (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Or (Eq (aLowerBoundOfIn0 a_2 a xT) False) (Eq (sdtlseqdt0 a_2 a_1) True))) % 20.08/20.27 Clause #393 (by superposition #[392, 69]): ∀ (a a_1 : Iota), % 20.08/20.27 Or (Eq (aInfimumOfIn0 a xS xT) False) % 20.08/20.27 (Or (Eq (aLowerBoundOfIn0 a_1 xS xT) False) (Or (Eq (sdtlseqdt0 a_1 a) True) (Eq False True))) % 20.08/20.27 Clause #396 (by clausification #[393]): ∀ (a a_1 : Iota), % 20.08/20.27 Or (Eq (aInfimumOfIn0 a xS xT) False) (Or (Eq (aLowerBoundOfIn0 a_1 xS xT) False) (Eq (sdtlseqdt0 a_1 a) True)) % 20.08/20.29 Clause #397 (by superposition #[396, 208]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Or (Eq (sdtlseqdt0 a xv) True) (Eq False True)) % 20.08/20.29 Clause #400 (by clausification #[397]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Eq (sdtlseqdt0 a xv) True) % 20.08/20.29 Clause #401 (by clausification #[384]): ∀ (a a_1 a_2 : Iota), % 20.08/20.29 Or (Eq (aSet0 a) False) % 20.08/20.29 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) (Eq (aLowerBoundOfIn0 a_2 a_1 a) True))) % 20.08/20.29 Clause #402 (by clausification #[384]): ∀ (a a_1 a_2 : Iota), % 20.08/20.29 Or (Eq (aSet0 a) False) % 20.08/20.29 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aInfimumOfIn0 a_2 a_1 a) False) (Eq (aElementOf0 a_2 a) True))) % 20.08/20.29 Clause #403 (by superposition #[401, 14]): ∀ (a a_1 : Iota), % 20.08/20.29 Or (Eq (aSubsetOf0 a xT) False) % 20.08/20.29 (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Or (Eq (aLowerBoundOfIn0 a_1 a xT) True) (Eq False True))) % 20.08/20.29 Clause #408 (by clausification #[403]): ∀ (a a_1 : Iota), % 20.08/20.29 Or (Eq (aSubsetOf0 a xT) False) (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Eq (aLowerBoundOfIn0 a_1 a xT) True)) % 20.08/20.29 Clause #409 (by superposition #[408, 69]): ∀ (a : Iota), Or (Eq (aInfimumOfIn0 a xS xT) False) (Or (Eq (aLowerBoundOfIn0 a xS xT) True) (Eq False True)) % 20.08/20.29 Clause #415 (by clausification #[409]): ∀ (a : Iota), Or (Eq (aInfimumOfIn0 a xS xT) False) (Eq (aLowerBoundOfIn0 a xS xT) True) % 20.08/20.29 Clause #416 (by superposition #[415, 208]): Or (Eq (aLowerBoundOfIn0 xv xS xT) True) (Eq False True) % 20.08/20.29 Clause #417 (by clausification #[416]): Eq (aLowerBoundOfIn0 xv xS xT) True % 20.08/20.29 Clause #418 (by superposition #[417, 230]): Or (Eq True False) (Eq (aElementOf0 xv xT) True) % 20.08/20.29 Clause #422 (by clausification #[418]): Eq (aElementOf0 xv xT) True % 20.08/20.29 Clause #423 (by superposition #[422, 51]): Or (Eq True False) (Eq (aElement0 xv) True) % 20.08/20.29 Clause #428 (by clausification #[423]): Eq (aElement0 xv) True % 20.08/20.29 Clause #429 (by superposition #[428, 42]): ∀ (a : Iota), % 20.08/20.29 Or (Eq True False) % 20.08/20.29 (Or (Eq (aElement0 a) False) (Or (Eq (sdtlseqdt0 xv a) False) (Or (Eq (sdtlseqdt0 a xv) False) (Eq xv a)))) % 20.08/20.29 Clause #437 (by clausification #[429]): ∀ (a : Iota), Or (Eq (aElement0 a) False) (Or (Eq (sdtlseqdt0 xv a) False) (Or (Eq (sdtlseqdt0 a xv) False) (Eq xv a))) % 20.08/20.29 Clause #443 (by superposition #[402, 14]): ∀ (a a_1 : Iota), % 20.08/20.29 Or (Eq (aSubsetOf0 a xT) False) % 20.08/20.29 (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Or (Eq (aElementOf0 a_1 xT) True) (Eq False True))) % 20.08/20.29 Clause #450 (by clausification #[443]): ∀ (a a_1 : Iota), % 20.08/20.29 Or (Eq (aSubsetOf0 a xT) False) (Or (Eq (aInfimumOfIn0 a_1 a xT) False) (Eq (aElementOf0 a_1 xT) True)) % 20.08/20.29 Clause #451 (by superposition #[450, 69]): ∀ (a : Iota), Or (Eq (aInfimumOfIn0 a xS xT) False) (Or (Eq (aElementOf0 a xT) True) (Eq False True)) % 20.08/20.29 Clause #454 (by clausification #[451]): ∀ (a : Iota), Or (Eq (aInfimumOfIn0 a xS xT) False) (Eq (aElementOf0 a xT) True) % 20.08/20.29 Clause #635 (by clausification #[209]): Eq % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) % 20.08/20.29 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0)) % 20.08/20.29 (aLowerBoundOfIn0 xu xS xT)) % 20.08/20.29 (∀ (W0 : Iota), % 20.08/20.29 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) % 20.08/20.29 (aLowerBoundOfIn0 W0 xS xT) → % 20.08/20.29 sdtlseqdt0 W0 xu)) % 20.08/20.29 (aInfimumOfIn0 xu xS xT)) % 20.08/20.29 (aElementOf0 xv xT)) % 20.08/20.29 (aElementOf0 xv xT)) % 20.08/20.29 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xv W0)) % 20.08/20.29 (aLowerBoundOfIn0 xv xS xT)) % 20.08/20.29 True % 20.08/20.29 Clause #3358 (by clausification #[635]): Eq % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And % 20.08/20.29 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0)) % 20.08/20.29 (aLowerBoundOfIn0 xu xS xT)) % 20.08/20.29 (∀ (W0 : Iota), % 20.08/20.29 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) % 20.08/20.29 (aLowerBoundOfIn0 W0 xS xT) → % 20.08/20.29 sdtlseqdt0 W0 xu)) % 20.08/20.29 (aInfimumOfIn0 xu xS xT)) % 20.17/20.33 (aElementOf0 xv xT)) % 20.17/20.33 (aElementOf0 xv xT)) % 20.17/20.33 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xv W0)) % 20.17/20.33 True % 20.17/20.33 Clause #3360 (by clausification #[3358]): Eq % 20.17/20.33 (And % 20.17/20.33 (And % 20.17/20.33 (And % 20.17/20.33 (And % 20.17/20.33 (And (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0)) % 20.17/20.33 (aLowerBoundOfIn0 xu xS xT)) % 20.17/20.33 (∀ (W0 : Iota), % 20.17/20.33 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) % 20.17/20.33 (aLowerBoundOfIn0 W0 xS xT) → % 20.17/20.33 sdtlseqdt0 W0 xu)) % 20.17/20.33 (aInfimumOfIn0 xu xS xT)) % 20.17/20.33 (aElementOf0 xv xT)) % 20.17/20.33 (aElementOf0 xv xT)) % 20.17/20.33 True % 20.17/20.33 Clause #3362 (by clausification #[3360]): Eq % 20.17/20.33 (And % 20.17/20.33 (And % 20.17/20.33 (And % 20.17/20.33 (And (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0)) % 20.17/20.33 (aLowerBoundOfIn0 xu xS xT)) % 20.17/20.33 (∀ (W0 : Iota), % 20.17/20.33 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) % 20.17/20.33 (aLowerBoundOfIn0 W0 xS xT) → % 20.17/20.33 sdtlseqdt0 W0 xu)) % 20.17/20.33 (aInfimumOfIn0 xu xS xT)) % 20.17/20.33 (aElementOf0 xv xT)) % 20.17/20.33 True % 20.17/20.33 Clause #3363 (by clausification #[3362]): Eq % 20.17/20.33 (And % 20.17/20.33 (And % 20.17/20.33 (And (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 xu W0)) % 20.17/20.33 (aLowerBoundOfIn0 xu xS xT)) % 20.17/20.33 (∀ (W0 : Iota), % 20.17/20.33 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W0 W1)) (aLowerBoundOfIn0 W0 xS xT) → % 20.17/20.33 sdtlseqdt0 W0 xu)) % 20.17/20.33 (aInfimumOfIn0 xu xS xT)) % 20.17/20.33 True % 20.17/20.33 Clause #3364 (by clausification #[3363]): Eq (aInfimumOfIn0 xu xS xT) True % 20.17/20.33 Clause #3366 (by superposition #[3364, 396]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Eq (sdtlseqdt0 a xu) True)) % 20.17/20.33 Clause #3367 (by superposition #[3364, 415]): Or (Eq True False) (Eq (aLowerBoundOfIn0 xu xS xT) True) % 20.17/20.33 Clause #3368 (by superposition #[3364, 454]): Or (Eq True False) (Eq (aElementOf0 xu xT) True) % 20.17/20.33 Clause #3370 (by clausification #[3368]): Eq (aElementOf0 xu xT) True % 20.17/20.33 Clause #3371 (by superposition #[3370, 51]): Or (Eq True False) (Eq (aElement0 xu) True) % 20.17/20.33 Clause #3390 (by clausification #[3371]): Eq (aElement0 xu) True % 20.17/20.33 Clause #3398 (by superposition #[3390, 437]): Or (Eq True False) (Or (Eq (sdtlseqdt0 xv xu) False) (Or (Eq (sdtlseqdt0 xu xv) False) (Eq xv xu))) % 20.17/20.33 Clause #3431 (by clausification #[3367]): Eq (aLowerBoundOfIn0 xu xS xT) True % 20.17/20.33 Clause #3433 (by superposition #[3431, 400]): Or (Eq True False) (Eq (sdtlseqdt0 xu xv) True) % 20.17/20.33 Clause #3434 (by clausification #[3433]): Eq (sdtlseqdt0 xu xv) True % 20.17/20.33 Clause #3461 (by clausification #[3366]): ∀ (a : Iota), Or (Eq (aLowerBoundOfIn0 a xS xT) False) (Eq (sdtlseqdt0 a xu) True) % 20.17/20.33 Clause #3462 (by superposition #[3461, 417]): Or (Eq (sdtlseqdt0 xv xu) True) (Eq False True) % 20.17/20.33 Clause #3464 (by clausification #[3462]): Eq (sdtlseqdt0 xv xu) True % 20.17/20.33 Clause #3465 (by clausification #[3398]): Or (Eq (sdtlseqdt0 xv xu) False) (Or (Eq (sdtlseqdt0 xu xv) False) (Eq xv xu)) % 20.17/20.33 Clause #3466 (by forward demodulation #[3465, 3434]): Or (Eq (sdtlseqdt0 xv xu) False) (Or (Eq True False) (Eq xv xu)) % 20.17/20.33 Clause #3467 (by clausification #[3466]): Or (Eq (sdtlseqdt0 xv xu) False) (Eq xv xu) % 20.17/20.33 Clause #3468 (by forward contextual literal cutting #[3467, 35]): Eq (sdtlseqdt0 xv xu) False % 20.17/20.33 Clause #3469 (by superposition #[3468, 3464]): Eq False True % 20.17/20.33 Clause #3471 (by clausification #[3469]): False % 20.17/20.33 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------