%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LAT381+3 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 07:53:32 PM UTC 2025 % Result : Theorem 23.58s 23.77s % Output : Proof 23.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : LAT381+3 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n007.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 : Thu Oct 2 19:11:38 EDT 2025 % 0.13/0.35 % CPUTime : % 23.58/23.77 SZS status Theorem for theBenchmark.p % 23.58/23.77 SZS output start Proof for theBenchmark.p % 23.58/23.77 Clause #2 (by assumption #[]): Eq (∀ (W0 : Iota), aSet0 W0 → ∀ (W1 : Iota), aElementOf0 W1 W0 → aElement0 W1) True % 23.58/23.77 Clause #7 (by assumption #[]): Eq (∀ (W0 W1 : Iota), And (aElement0 W0) (aElement0 W1) → And (sdtlseqdt0 W0 W1) (sdtlseqdt0 W1 W0) → Eq W0 W1) True % 23.58/23.77 Clause #10 (by assumption #[]): Eq % 23.58/23.77 (∀ (W0 : Iota), % 23.58/23.77 aSet0 W0 → % 23.58/23.77 ∀ (W1 : Iota), % 23.58/23.77 aSubsetOf0 W1 W0 → % 23.58/23.77 ∀ (W2 : Iota), % 23.58/23.77 Iff (aUpperBoundOfIn0 W2 W1 W0) % 23.58/23.77 (And (aElementOf0 W2 W0) (∀ (W3 : Iota), aElementOf0 W3 W1 → sdtlseqdt0 W3 W2))) % 23.58/23.77 True % 23.58/23.77 Clause #12 (by assumption #[]): Eq % 23.58/23.77 (∀ (W0 : Iota), % 23.58/23.77 aSet0 W0 → % 23.58/23.77 ∀ (W1 : Iota), % 23.58/23.77 aSubsetOf0 W1 W0 → % 23.58/23.77 ∀ (W2 : Iota), % 23.58/23.77 Iff (aSupremumOfIn0 W2 W1 W0) % 23.58/23.77 (And (And (aElementOf0 W2 W0) (aUpperBoundOfIn0 W2 W1 W0)) % 23.58/23.77 (∀ (W3 : Iota), aUpperBoundOfIn0 W3 W1 W0 → sdtlseqdt0 W2 W3))) % 23.58/23.77 True % 23.58/23.77 Clause #13 (by assumption #[]): Eq (aSet0 xT) True % 23.58/23.77 Clause #14 (by assumption #[]): Eq (And (And (aSet0 xS) (∀ (W0 : Iota), aElementOf0 W0 xS → aElementOf0 W0 xT)) (aSubsetOf0 xS xT)) True % 23.58/23.77 Clause #15 (by assumption #[]): Eq % 23.58/23.77 (And % 23.58/23.77 (And % 23.58/23.77 (And % 23.58/23.77 (And % 23.58/23.77 (And % 23.58/23.77 (And % 23.58/23.77 (And % 23.58/23.77 (And % 23.58/23.77 (And % 23.58/23.77 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) % 23.58/23.77 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xu)) % 23.58/23.77 (aUpperBoundOfIn0 xu xS xT)) % 23.58/23.77 (∀ (W0 : Iota), % 23.58/23.77 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W1 W0)) % 23.58/23.77 (aUpperBoundOfIn0 W0 xS xT) → % 23.58/23.77 sdtlseqdt0 xu W0)) % 23.58/23.77 (aSupremumOfIn0 xu xS xT)) % 23.58/23.77 (aElementOf0 xv xT)) % 23.58/23.77 (aElementOf0 xv xT)) % 23.58/23.77 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xv)) % 23.58/23.77 (aUpperBoundOfIn0 xv xS xT)) % 23.58/23.77 (∀ (W0 : Iota), % 23.58/23.77 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W1 W0)) (aUpperBoundOfIn0 W0 xS xT) → % 23.58/23.77 sdtlseqdt0 xv W0)) % 23.58/23.77 (aSupremumOfIn0 xv xS xT)) % 23.58/23.77 True % 23.58/23.77 Clause #16 (by assumption #[]): Eq (Not (Eq xu xv)) True % 23.58/23.77 Clause #28 (by clausification #[2]): ∀ (a : Iota), Eq (aSet0 a → ∀ (W1 : Iota), aElementOf0 W1 a → aElement0 W1) True % 23.58/23.77 Clause #29 (by clausification #[28]): ∀ (a : Iota), Or (Eq (aSet0 a) False) (Eq (∀ (W1 : Iota), aElementOf0 W1 a → aElement0 W1) True) % 23.58/23.77 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (aSet0 a) False) (Eq (aElementOf0 a_1 a → aElement0 a_1) True) % 23.58/23.77 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Or (Eq (aSet0 a) False) (Or (Eq (aElementOf0 a_1 a) False) (Eq (aElement0 a_1) True)) % 23.58/23.77 Clause #32 (by superposition #[31, 13]): ∀ (a : Iota), Or (Eq (aElementOf0 a xT) False) (Or (Eq (aElement0 a) True) (Eq False True)) % 23.58/23.77 Clause #33 (by clausification #[16]): Eq (Eq xu xv) False % 23.58/23.77 Clause #34 (by clausification #[33]): Ne xu xv % 23.58/23.77 Clause #35 (by clausification #[32]): ∀ (a : Iota), Or (Eq (aElementOf0 a xT) False) (Eq (aElement0 a) True) % 23.58/23.77 Clause #36 (by clausification #[7]): ∀ (a : Iota), % 23.58/23.77 Eq (∀ (W1 : Iota), And (aElement0 a) (aElement0 W1) → And (sdtlseqdt0 a W1) (sdtlseqdt0 W1 a) → Eq a W1) True % 23.58/23.77 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 % 23.58/23.77 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 23.58/23.77 Or (Eq (And (aElement0 a) (aElement0 a_1)) False) (Eq (And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a) → Eq a a_1) True) % 23.58/23.77 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 23.58/23.77 Or (Eq (And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a) → Eq a a_1) True) % 23.58/23.77 (Or (Eq (aElement0 a) False) (Eq (aElement0 a_1) False)) % 23.58/23.77 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 23.58/23.77 Or (Eq (aElement0 a) False) % 23.58/23.77 (Or (Eq (aElement0 a_1) False) (Or (Eq (And (sdtlseqdt0 a a_1) (sdtlseqdt0 a_1 a)) False) (Eq (Eq a a_1) True))) % 23.58/23.80 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 23.58/23.80 Or (Eq (aElement0 a) False) % 23.58/23.80 (Or (Eq (aElement0 a_1) False) % 23.58/23.80 (Or (Eq (Eq a a_1) True) (Or (Eq (sdtlseqdt0 a a_1) False) (Eq (sdtlseqdt0 a_1 a) False)))) % 23.58/23.80 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 23.58/23.80 Or (Eq (aElement0 a) False) % 23.58/23.80 (Or (Eq (aElement0 a_1) False) (Or (Eq (sdtlseqdt0 a a_1) False) (Or (Eq (sdtlseqdt0 a_1 a) False) (Eq a a_1)))) % 23.58/23.80 Clause #51 (by clausification #[14]): Eq (aSubsetOf0 xS xT) True % 23.58/23.80 Clause #124 (by clausification #[10]): ∀ (a : Iota), % 23.58/23.80 Eq % 23.58/23.80 (aSet0 a → % 23.58/23.80 ∀ (W1 : Iota), % 23.58/23.80 aSubsetOf0 W1 a → % 23.58/23.80 ∀ (W2 : Iota), % 23.58/23.80 Iff (aUpperBoundOfIn0 W2 W1 a) % 23.58/23.80 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 W1 → sdtlseqdt0 W3 W2))) % 23.58/23.80 True % 23.58/23.80 Clause #125 (by clausification #[124]): ∀ (a : Iota), % 23.58/23.80 Or (Eq (aSet0 a) False) % 23.58/23.80 (Eq % 23.58/23.80 (∀ (W1 : Iota), % 23.58/23.80 aSubsetOf0 W1 a → % 23.58/23.80 ∀ (W2 : Iota), % 23.58/23.80 Iff (aUpperBoundOfIn0 W2 W1 a) % 23.58/23.80 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 W1 → sdtlseqdt0 W3 W2))) % 23.58/23.80 True) % 23.58/23.80 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), % 23.58/23.80 Or (Eq (aSet0 a) False) % 23.58/23.80 (Eq % 23.58/23.80 (aSubsetOf0 a_1 a → % 23.58/23.80 ∀ (W2 : Iota), % 23.58/23.80 Iff (aUpperBoundOfIn0 W2 a_1 a) % 23.58/23.80 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 W3 W2))) % 23.58/23.80 True) % 23.58/23.80 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), % 23.58/23.80 Or (Eq (aSet0 a) False) % 23.58/23.80 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.58/23.80 (Eq % 23.58/23.80 (∀ (W2 : Iota), % 23.58/23.80 Iff (aUpperBoundOfIn0 W2 a_1 a) % 23.58/23.80 (And (aElementOf0 W2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 W3 W2))) % 23.58/23.80 True)) % 23.58/23.80 Clause #128 (by clausification #[127]): ∀ (a a_1 a_2 : Iota), % 23.58/23.80 Or (Eq (aSet0 a) False) % 23.58/23.80 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.58/23.80 (Eq % 23.58/23.80 (Iff (aUpperBoundOfIn0 a_2 a_1 a) % 23.58/23.80 (And (aElementOf0 a_2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 W3 a_2))) % 23.58/23.80 True)) % 23.58/23.80 Clause #130 (by clausification #[128]): ∀ (a a_1 a_2 : Iota), % 23.58/23.80 Or (Eq (aSet0 a) False) % 23.58/23.80 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.58/23.80 (Or (Eq (aUpperBoundOfIn0 a_2 a_1 a) False) % 23.58/23.80 (Eq (And (aElementOf0 a_2 a) (∀ (W3 : Iota), aElementOf0 W3 a_1 → sdtlseqdt0 W3 a_2)) True))) % 23.58/23.80 Clause #170 (by clausification #[12]): ∀ (a : Iota), % 23.58/23.80 Eq % 23.58/23.80 (aSet0 a → % 23.58/23.80 ∀ (W1 : Iota), % 23.58/23.80 aSubsetOf0 W1 a → % 23.58/23.80 ∀ (W2 : Iota), % 23.58/23.80 Iff (aSupremumOfIn0 W2 W1 a) % 23.58/23.80 (And (And (aElementOf0 W2 a) (aUpperBoundOfIn0 W2 W1 a)) % 23.58/23.80 (∀ (W3 : Iota), aUpperBoundOfIn0 W3 W1 a → sdtlseqdt0 W2 W3))) % 23.58/23.80 True % 23.58/23.80 Clause #171 (by clausification #[170]): ∀ (a : Iota), % 23.58/23.80 Or (Eq (aSet0 a) False) % 23.58/23.80 (Eq % 23.58/23.80 (∀ (W1 : Iota), % 23.58/23.80 aSubsetOf0 W1 a → % 23.58/23.80 ∀ (W2 : Iota), % 23.58/23.80 Iff (aSupremumOfIn0 W2 W1 a) % 23.58/23.80 (And (And (aElementOf0 W2 a) (aUpperBoundOfIn0 W2 W1 a)) % 23.58/23.80 (∀ (W3 : Iota), aUpperBoundOfIn0 W3 W1 a → sdtlseqdt0 W2 W3))) % 23.58/23.80 True) % 23.58/23.80 Clause #172 (by clausification #[171]): ∀ (a a_1 : Iota), % 23.58/23.80 Or (Eq (aSet0 a) False) % 23.58/23.80 (Eq % 23.58/23.80 (aSubsetOf0 a_1 a → % 23.58/23.80 ∀ (W2 : Iota), % 23.58/23.80 Iff (aSupremumOfIn0 W2 a_1 a) % 23.58/23.80 (And (And (aElementOf0 W2 a) (aUpperBoundOfIn0 W2 a_1 a)) % 23.58/23.80 (∀ (W3 : Iota), aUpperBoundOfIn0 W3 a_1 a → sdtlseqdt0 W2 W3))) % 23.58/23.80 True) % 23.58/23.80 Clause #173 (by clausification #[172]): ∀ (a a_1 : Iota), % 23.58/23.80 Or (Eq (aSet0 a) False) % 23.58/23.80 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.58/23.80 (Eq % 23.58/23.80 (∀ (W2 : Iota), % 23.58/23.80 Iff (aSupremumOfIn0 W2 a_1 a) % 23.58/23.80 (And (And (aElementOf0 W2 a) (aUpperBoundOfIn0 W2 a_1 a)) % 23.58/23.80 (∀ (W3 : Iota), aUpperBoundOfIn0 W3 a_1 a → sdtlseqdt0 W2 W3))) % 23.58/23.80 True)) % 23.58/23.80 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 : Iota), % 23.58/23.80 Or (Eq (aSet0 a) False) % 23.58/23.80 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.58/23.80 (Eq % 23.58/23.80 (Iff (aSupremumOfIn0 a_2 a_1 a) % 23.58/23.80 (And (And (aElementOf0 a_2 a) (aUpperBoundOfIn0 a_2 a_1 a)) % 23.58/23.80 (∀ (W3 : Iota), aUpperBoundOfIn0 W3 a_1 a → sdtlseqdt0 a_2 W3))) % 23.65/23.82 True)) % 23.65/23.82 Clause #176 (by clausification #[174]): ∀ (a a_1 a_2 : Iota), % 23.65/23.82 Or (Eq (aSet0 a) False) % 23.65/23.82 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.65/23.82 (Or (Eq (aSupremumOfIn0 a_2 a_1 a) False) % 23.65/23.82 (Eq % 23.65/23.82 (And (And (aElementOf0 a_2 a) (aUpperBoundOfIn0 a_2 a_1 a)) % 23.65/23.82 (∀ (W3 : Iota), aUpperBoundOfIn0 W3 a_1 a → sdtlseqdt0 a_2 W3)) % 23.65/23.82 True))) % 23.65/23.82 Clause #188 (by clausification #[130]): ∀ (a a_1 a_2 : Iota), % 23.65/23.82 Or (Eq (aSet0 a) False) % 23.65/23.82 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aUpperBoundOfIn0 a_2 a_1 a) False) (Eq (aElementOf0 a_2 a) True))) % 23.65/23.82 Clause #193 (by superposition #[188, 13]): ∀ (a a_1 : Iota), % 23.65/23.82 Or (Eq (aSubsetOf0 a xT) False) % 23.65/23.82 (Or (Eq (aUpperBoundOfIn0 a_1 a xT) False) (Or (Eq (aElementOf0 a_1 xT) True) (Eq False True))) % 23.65/23.82 Clause #196 (by clausification #[15]): Eq (aSupremumOfIn0 xv xS xT) True % 23.65/23.82 Clause #197 (by clausification #[15]): Eq % 23.65/23.82 (And % 23.65/23.82 (And % 23.65/23.82 (And % 23.65/23.82 (And % 23.65/23.82 (And % 23.65/23.82 (And % 23.65/23.82 (And % 23.65/23.82 (And % 23.65/23.82 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) % 23.65/23.82 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xu)) % 23.65/23.82 (aUpperBoundOfIn0 xu xS xT)) % 23.65/23.82 (∀ (W0 : Iota), % 23.65/23.82 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W1 W0)) % 23.65/23.82 (aUpperBoundOfIn0 W0 xS xT) → % 23.65/23.82 sdtlseqdt0 xu W0)) % 23.65/23.82 (aSupremumOfIn0 xu xS xT)) % 23.65/23.82 (aElementOf0 xv xT)) % 23.65/23.82 (aElementOf0 xv xT)) % 23.65/23.82 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xv)) % 23.65/23.82 (aUpperBoundOfIn0 xv xS xT)) % 23.65/23.82 (∀ (W0 : Iota), % 23.65/23.82 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W1 W0)) (aUpperBoundOfIn0 W0 xS xT) → % 23.65/23.82 sdtlseqdt0 xv W0)) % 23.65/23.82 True % 23.65/23.82 Clause #198 (by clausification #[193]): ∀ (a a_1 : Iota), % 23.65/23.82 Or (Eq (aSubsetOf0 a xT) False) (Or (Eq (aUpperBoundOfIn0 a_1 a xT) False) (Eq (aElementOf0 a_1 xT) True)) % 23.65/23.82 Clause #199 (by superposition #[198, 51]): ∀ (a : Iota), Or (Eq (aUpperBoundOfIn0 a xS xT) False) (Or (Eq (aElementOf0 a xT) True) (Eq False True)) % 23.65/23.82 Clause #200 (by clausification #[199]): ∀ (a : Iota), Or (Eq (aUpperBoundOfIn0 a xS xT) False) (Eq (aElementOf0 a xT) True) % 23.65/23.82 Clause #345 (by clausification #[176]): ∀ (a a_1 a_2 : Iota), % 23.65/23.82 Or (Eq (aSet0 a) False) % 23.65/23.82 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.65/23.82 (Or (Eq (aSupremumOfIn0 a_2 a_1 a) False) % 23.65/23.82 (Eq (∀ (W3 : Iota), aUpperBoundOfIn0 W3 a_1 a → sdtlseqdt0 a_2 W3) True))) % 23.65/23.82 Clause #346 (by clausification #[176]): ∀ (a a_1 a_2 : Iota), % 23.65/23.82 Or (Eq (aSet0 a) False) % 23.65/23.82 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.65/23.82 (Or (Eq (aSupremumOfIn0 a_2 a_1 a) False) (Eq (And (aElementOf0 a_2 a) (aUpperBoundOfIn0 a_2 a_1 a)) True))) % 23.65/23.82 Clause #347 (by clausification #[345]): ∀ (a a_1 a_2 a_3 : Iota), % 23.65/23.82 Or (Eq (aSet0 a) False) % 23.65/23.82 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.65/23.82 (Or (Eq (aSupremumOfIn0 a_2 a_1 a) False) (Eq (aUpperBoundOfIn0 a_3 a_1 a → sdtlseqdt0 a_2 a_3) True))) % 23.65/23.82 Clause #348 (by clausification #[347]): ∀ (a a_1 a_2 a_3 : Iota), % 23.65/23.82 Or (Eq (aSet0 a) False) % 23.65/23.82 (Or (Eq (aSubsetOf0 a_1 a) False) % 23.65/23.82 (Or (Eq (aSupremumOfIn0 a_2 a_1 a) False) % 23.65/23.82 (Or (Eq (aUpperBoundOfIn0 a_3 a_1 a) False) (Eq (sdtlseqdt0 a_2 a_3) True)))) % 23.65/23.82 Clause #349 (by superposition #[348, 13]): ∀ (a a_1 a_2 : Iota), % 23.65/23.82 Or (Eq (aSubsetOf0 a xT) False) % 23.65/23.82 (Or (Eq (aSupremumOfIn0 a_1 a xT) False) % 23.65/23.82 (Or (Eq (aUpperBoundOfIn0 a_2 a xT) False) (Or (Eq (sdtlseqdt0 a_1 a_2) True) (Eq False True)))) % 23.65/23.82 Clause #356 (by clausification #[349]): ∀ (a a_1 a_2 : Iota), % 23.65/23.82 Or (Eq (aSubsetOf0 a xT) False) % 23.65/23.82 (Or (Eq (aSupremumOfIn0 a_1 a xT) False) (Or (Eq (aUpperBoundOfIn0 a_2 a xT) False) (Eq (sdtlseqdt0 a_1 a_2) True))) % 23.65/23.82 Clause #357 (by superposition #[356, 51]): ∀ (a a_1 : Iota), % 23.65/23.82 Or (Eq (aSupremumOfIn0 a xS xT) False) % 23.65/23.82 (Or (Eq (aUpperBoundOfIn0 a_1 xS xT) False) (Or (Eq (sdtlseqdt0 a a_1) True) (Eq False True))) % 23.65/23.82 Clause #360 (by clausification #[357]): ∀ (a a_1 : Iota), % 23.65/23.82 Or (Eq (aSupremumOfIn0 a xS xT) False) (Or (Eq (aUpperBoundOfIn0 a_1 xS xT) False) (Eq (sdtlseqdt0 a a_1) True)) % 23.65/23.84 Clause #361 (by superposition #[360, 196]): ∀ (a : Iota), Or (Eq (aUpperBoundOfIn0 a xS xT) False) (Or (Eq (sdtlseqdt0 xv a) True) (Eq False True)) % 23.65/23.84 Clause #362 (by clausification #[361]): ∀ (a : Iota), Or (Eq (aUpperBoundOfIn0 a xS xT) False) (Eq (sdtlseqdt0 xv a) True) % 23.65/23.84 Clause #365 (by clausification #[346]): ∀ (a a_1 a_2 : Iota), % 23.65/23.84 Or (Eq (aSet0 a) False) % 23.65/23.84 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aSupremumOfIn0 a_2 a_1 a) False) (Eq (aUpperBoundOfIn0 a_2 a_1 a) True))) % 23.65/23.84 Clause #366 (by clausification #[346]): ∀ (a a_1 a_2 : Iota), % 23.65/23.84 Or (Eq (aSet0 a) False) % 23.65/23.84 (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aSupremumOfIn0 a_2 a_1 a) False) (Eq (aElementOf0 a_2 a) True))) % 23.65/23.84 Clause #367 (by superposition #[365, 13]): ∀ (a a_1 : Iota), % 23.65/23.84 Or (Eq (aSubsetOf0 a xT) False) % 23.65/23.84 (Or (Eq (aSupremumOfIn0 a_1 a xT) False) (Or (Eq (aUpperBoundOfIn0 a_1 a xT) True) (Eq False True))) % 23.65/23.84 Clause #372 (by clausification #[367]): ∀ (a a_1 : Iota), % 23.65/23.84 Or (Eq (aSubsetOf0 a xT) False) (Or (Eq (aSupremumOfIn0 a_1 a xT) False) (Eq (aUpperBoundOfIn0 a_1 a xT) True)) % 23.65/23.84 Clause #373 (by superposition #[372, 51]): ∀ (a : Iota), Or (Eq (aSupremumOfIn0 a xS xT) False) (Or (Eq (aUpperBoundOfIn0 a xS xT) True) (Eq False True)) % 23.65/23.84 Clause #379 (by clausification #[373]): ∀ (a : Iota), Or (Eq (aSupremumOfIn0 a xS xT) False) (Eq (aUpperBoundOfIn0 a xS xT) True) % 23.65/23.84 Clause #380 (by superposition #[379, 196]): Or (Eq (aUpperBoundOfIn0 xv xS xT) True) (Eq False True) % 23.65/23.84 Clause #381 (by clausification #[380]): Eq (aUpperBoundOfIn0 xv xS xT) True % 23.65/23.84 Clause #382 (by superposition #[381, 200]): Or (Eq True False) (Eq (aElementOf0 xv xT) True) % 23.65/23.84 Clause #386 (by clausification #[382]): Eq (aElementOf0 xv xT) True % 23.65/23.84 Clause #387 (by superposition #[386, 35]): Or (Eq True False) (Eq (aElement0 xv) True) % 23.65/23.84 Clause #390 (by clausification #[387]): Eq (aElement0 xv) True % 23.65/23.84 Clause #391 (by superposition #[390, 42]): ∀ (a : Iota), % 23.65/23.84 Or (Eq True False) % 23.65/23.84 (Or (Eq (aElement0 a) False) (Or (Eq (sdtlseqdt0 xv a) False) (Or (Eq (sdtlseqdt0 a xv) False) (Eq xv a)))) % 23.65/23.84 Clause #401 (by clausification #[391]): ∀ (a : Iota), Or (Eq (aElement0 a) False) (Or (Eq (sdtlseqdt0 xv a) False) (Or (Eq (sdtlseqdt0 a xv) False) (Eq xv a))) % 23.65/23.84 Clause #408 (by superposition #[366, 13]): ∀ (a a_1 : Iota), % 23.65/23.84 Or (Eq (aSubsetOf0 a xT) False) % 23.65/23.84 (Or (Eq (aSupremumOfIn0 a_1 a xT) False) (Or (Eq (aElementOf0 a_1 xT) True) (Eq False True))) % 23.65/23.84 Clause #415 (by clausification #[408]): ∀ (a a_1 : Iota), % 23.65/23.84 Or (Eq (aSubsetOf0 a xT) False) (Or (Eq (aSupremumOfIn0 a_1 a xT) False) (Eq (aElementOf0 a_1 xT) True)) % 23.65/23.84 Clause #416 (by superposition #[415, 51]): ∀ (a : Iota), Or (Eq (aSupremumOfIn0 a xS xT) False) (Or (Eq (aElementOf0 a xT) True) (Eq False True)) % 23.65/23.84 Clause #419 (by clausification #[416]): ∀ (a : Iota), Or (Eq (aSupremumOfIn0 a xS xT) False) (Eq (aElementOf0 a xT) True) % 23.65/23.84 Clause #539 (by clausification #[197]): Eq % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) % 23.65/23.84 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xu)) % 23.65/23.84 (aUpperBoundOfIn0 xu xS xT)) % 23.65/23.84 (∀ (W0 : Iota), % 23.65/23.84 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W1 W0)) % 23.65/23.84 (aUpperBoundOfIn0 W0 xS xT) → % 23.65/23.84 sdtlseqdt0 xu W0)) % 23.65/23.84 (aSupremumOfIn0 xu xS xT)) % 23.65/23.84 (aElementOf0 xv xT)) % 23.65/23.84 (aElementOf0 xv xT)) % 23.65/23.84 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xv)) % 23.65/23.84 (aUpperBoundOfIn0 xv xS xT)) % 23.65/23.84 True % 23.65/23.84 Clause #3327 (by clausification #[539]): Eq % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And % 23.65/23.84 (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xu)) % 23.65/23.84 (aUpperBoundOfIn0 xu xS xT)) % 23.65/23.84 (∀ (W0 : Iota), % 23.65/23.84 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W1 W0)) % 23.65/23.84 (aUpperBoundOfIn0 W0 xS xT) → % 23.65/23.84 sdtlseqdt0 xu W0)) % 23.72/23.89 (aSupremumOfIn0 xu xS xT)) % 23.72/23.89 (aElementOf0 xv xT)) % 23.72/23.89 (aElementOf0 xv xT)) % 23.72/23.89 (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xv)) % 23.72/23.89 True % 23.72/23.89 Clause #3329 (by clausification #[3327]): Eq % 23.72/23.89 (And % 23.72/23.89 (And % 23.72/23.89 (And % 23.72/23.89 (And % 23.72/23.89 (And (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xu)) % 23.72/23.89 (aUpperBoundOfIn0 xu xS xT)) % 23.72/23.89 (∀ (W0 : Iota), % 23.72/23.89 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W1 W0)) % 23.72/23.89 (aUpperBoundOfIn0 W0 xS xT) → % 23.72/23.89 sdtlseqdt0 xu W0)) % 23.72/23.89 (aSupremumOfIn0 xu xS xT)) % 23.72/23.89 (aElementOf0 xv xT)) % 23.72/23.89 (aElementOf0 xv xT)) % 23.72/23.89 True % 23.72/23.89 Clause #3331 (by clausification #[3329]): Eq % 23.72/23.89 (And % 23.72/23.89 (And % 23.72/23.89 (And % 23.72/23.89 (And (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xu)) % 23.72/23.89 (aUpperBoundOfIn0 xu xS xT)) % 23.72/23.89 (∀ (W0 : Iota), % 23.72/23.89 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W1 W0)) % 23.72/23.89 (aUpperBoundOfIn0 W0 xS xT) → % 23.72/23.89 sdtlseqdt0 xu W0)) % 23.72/23.89 (aSupremumOfIn0 xu xS xT)) % 23.72/23.89 (aElementOf0 xv xT)) % 23.72/23.89 True % 23.72/23.89 Clause #3332 (by clausification #[3331]): Eq % 23.72/23.89 (And % 23.72/23.89 (And % 23.72/23.89 (And (And (And (aElementOf0 xu xT) (aElementOf0 xu xT)) (∀ (W0 : Iota), aElementOf0 W0 xS → sdtlseqdt0 W0 xu)) % 23.72/23.89 (aUpperBoundOfIn0 xu xS xT)) % 23.72/23.89 (∀ (W0 : Iota), % 23.72/23.89 Or (And (aElementOf0 W0 xT) (∀ (W1 : Iota), aElementOf0 W1 xS → sdtlseqdt0 W1 W0)) (aUpperBoundOfIn0 W0 xS xT) → % 23.72/23.89 sdtlseqdt0 xu W0)) % 23.72/23.89 (aSupremumOfIn0 xu xS xT)) % 23.72/23.89 True % 23.72/23.89 Clause #3333 (by clausification #[3332]): Eq (aSupremumOfIn0 xu xS xT) True % 23.72/23.89 Clause #3335 (by superposition #[3333, 360]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (aUpperBoundOfIn0 a xS xT) False) (Eq (sdtlseqdt0 xu a) True)) % 23.72/23.89 Clause #3336 (by superposition #[3333, 379]): Or (Eq True False) (Eq (aUpperBoundOfIn0 xu xS xT) True) % 23.72/23.89 Clause #3337 (by superposition #[3333, 419]): Or (Eq True False) (Eq (aElementOf0 xu xT) True) % 23.72/23.89 Clause #3339 (by clausification #[3337]): Eq (aElementOf0 xu xT) True % 23.72/23.89 Clause #3340 (by superposition #[3339, 35]): Or (Eq True False) (Eq (aElement0 xu) True) % 23.72/23.89 Clause #3359 (by clausification #[3340]): Eq (aElement0 xu) True % 23.72/23.89 Clause #3367 (by superposition #[3359, 401]): Or (Eq True False) (Or (Eq (sdtlseqdt0 xv xu) False) (Or (Eq (sdtlseqdt0 xu xv) False) (Eq xv xu))) % 23.72/23.89 Clause #3400 (by clausification #[3336]): Eq (aUpperBoundOfIn0 xu xS xT) True % 23.72/23.89 Clause #3402 (by superposition #[3400, 362]): Or (Eq True False) (Eq (sdtlseqdt0 xv xu) True) % 23.72/23.89 Clause #3403 (by clausification #[3402]): Eq (sdtlseqdt0 xv xu) True % 23.72/23.89 Clause #3430 (by clausification #[3335]): ∀ (a : Iota), Or (Eq (aUpperBoundOfIn0 a xS xT) False) (Eq (sdtlseqdt0 xu a) True) % 23.72/23.89 Clause #3431 (by superposition #[3430, 381]): Or (Eq (sdtlseqdt0 xu xv) True) (Eq False True) % 23.72/23.89 Clause #3433 (by clausification #[3431]): Eq (sdtlseqdt0 xu xv) True % 23.72/23.89 Clause #3434 (by clausification #[3367]): Or (Eq (sdtlseqdt0 xv xu) False) (Or (Eq (sdtlseqdt0 xu xv) False) (Eq xv xu)) % 23.72/23.89 Clause #3435 (by forward demodulation #[3434, 3433]): Or (Eq (sdtlseqdt0 xv xu) False) (Or (Eq True False) (Eq xv xu)) % 23.72/23.89 Clause #3436 (by clausification #[3435]): Or (Eq (sdtlseqdt0 xv xu) False) (Eq xv xu) % 23.72/23.89 Clause #3437 (by forward contextual literal cutting #[3436, 34]): Eq (sdtlseqdt0 xv xu) False % 23.72/23.89 Clause #3438 (by superposition #[3437, 3403]): Eq False True % 23.72/23.89 Clause #3440 (by clausification #[3438]): False % 23.72/23.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------