0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : duper %s 0.13/0.35 % Computer : n013.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1440 0.13/0.35 % WCLimit : 180 0.13/0.35 % DateTime : Mon Jul 3 04:13:47 EDT 2023 0.13/0.35 % CPUTime : 8.97/9.18 SZS status Theorem for theBenchmark.p 8.97/9.18 SZS output start Proof for theBenchmark.p 8.97/9.18 Clause #0 (by assumption #[]): Eq 8.97/9.18 (Not 8.97/9.18 (Not 8.97/9.18 (And 8.97/9.18 (And 8.97/9.18 (And 8.97/9.18 (And (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) 8.97/9.18 (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) 8.97/9.18 (∀ (Xp Xq : Iota), Or (Or (cT Xq) (Not (cT Xp))) (Not (cT (imp Xp Xq))))))) 8.97/9.18 True 8.97/9.18 Clause #1 (by clausification #[0]): Eq 8.97/9.18 (Not 8.97/9.18 (And 8.97/9.18 (And 8.97/9.18 (And 8.97/9.18 (And (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) 8.97/9.18 (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) 8.97/9.18 (∀ (Xp Xq : Iota), Or (Or (cT Xq) (Not (cT Xp))) (Not (cT (imp Xp Xq)))))) 8.97/9.18 False 8.97/9.18 Clause #2 (by clausification #[1]): Eq 8.97/9.18 (And 8.97/9.18 (And 8.97/9.18 (And 8.97/9.18 (And (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) 8.97/9.18 (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) 8.97/9.18 (∀ (Xp Xq : Iota), Or (Or (cT Xq) (Not (cT Xp))) (Not (cT (imp Xp Xq))))) 8.97/9.18 True 8.97/9.18 Clause #3 (by clausification #[2]): Eq (∀ (Xp Xq : Iota), Or (Or (cT Xq) (Not (cT Xp))) (Not (cT (imp Xp Xq)))) True 8.97/9.18 Clause #4 (by clausification #[2]): Eq 8.97/9.18 (And 8.97/9.18 (And 8.97/9.18 (And (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) 8.97/9.18 (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) 8.97/9.18 True 8.97/9.18 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Xq : Iota), Or (Or (cT Xq) (Not (cT a))) (Not (cT (imp a Xq)))) True 8.97/9.18 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (Or (Or (cT a) (Not (cT a_1))) (Not (cT (imp a_1 a)))) True 8.97/9.18 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (Or (cT a) (Not (cT a_1))) True) (Eq (Not (cT (imp a_1 a))) True) 8.97/9.18 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (Not (cT (imp a a_1))) True) (Or (Eq (cT a_1) True) (Eq (Not (cT a)) True)) 8.97/9.18 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (cT a) True) (Or (Eq (Not (cT a_1)) True) (Eq (cT (imp a_1 a)) False)) 8.97/9.18 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq (cT a) True) (Or (Eq (cT (imp a_1 a)) False) (Eq (cT a_1) False)) 8.97/9.18 Clause #11 (by clausification #[4]): Eq (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp))) True 8.97/9.18 Clause #12 (by clausification #[4]): Eq 8.97/9.18 (And 8.97/9.18 (And (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) 8.97/9.18 (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa)))) 8.97/9.18 True 8.97/9.18 Clause #13 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Xq : Iota), cT (imp a (imp Xq a))) True 8.97/9.18 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (cT (imp a (imp a_1 a))) True 8.97/9.18 Clause #15 (by superposition #[14, 10]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a_1)) True) (Or (Eq True False) (Eq (cT a_1) False)) 8.97/9.18 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a_1)) True) (Eq (cT a_1) False) 8.97/9.18 Clause #17 (by superposition #[16, 14]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp a (imp a_1 (imp a_2 a_1)))) True) (Eq False True) 8.97/9.18 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp a (imp a_1 (imp a_2 a_1)))) True 8.97/9.18 Clause #22 (by clausification #[12]): Eq (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa))) True 8.97/9.18 Clause #23 (by clausification #[12]): Eq 8.97/9.18 (And (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr)))) 8.97/9.18 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) 8.97/9.18 True 8.97/9.18 Clause #24 (by clausification #[22]): ∀ (a : Iota), Eq (Not (cT (imp (nt (nt (skS.0 0 a))) (skS.0 0 a)))) True 9.03/9.21 Clause #25 (by clausification #[24]): ∀ (a : Iota), Eq (cT (imp (nt (nt (skS.0 0 a))) (skS.0 0 a))) False 9.03/9.21 Clause #37 (by clausification #[23]): Eq (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp))) True 9.03/9.21 Clause #38 (by clausification #[23]): Eq (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr)))) True 9.03/9.21 Clause #39 (by clausification #[37]): ∀ (a : Iota), Eq (∀ (Xq : Iota), cT (imp (imp (nt a) (nt Xq)) (imp Xq a))) True 9.03/9.21 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (cT (imp (imp (nt a) (nt a_1)) (imp a_1 a))) True 9.03/9.21 Clause #42 (by superposition #[40, 16]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp a (imp (imp (nt a_1) (nt a_2)) (imp a_2 a_1)))) True) (Eq True False) 9.03/9.21 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp a (imp (imp (nt a_1) (nt a_2)) (imp a_2 a_1)))) True 9.03/9.21 Clause #55 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (Xq Xr : Iota), cT (imp (imp a (imp Xq Xr)) (imp (imp a Xq) (imp a Xr)))) True 9.03/9.21 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), Eq (∀ (Xr : Iota), cT (imp (imp a (imp a_1 Xr)) (imp (imp a a_1) (imp a Xr)))) True 9.03/9.21 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp a (imp a_1 a_2)) (imp (imp a a_1) (imp a a_2)))) True 9.03/9.21 Clause #58 (by superposition #[57, 10]): ∀ (a a_1 a_2 : Iota), 9.03/9.21 Or (Eq (cT (imp (imp a a_1) (imp a a_2))) True) (Or (Eq True False) (Eq (cT (imp a (imp a_1 a_2))) False)) 9.03/9.21 Clause #60 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp (imp a a_1) (imp a a_2))) True) (Eq (cT (imp a (imp a_1 a_2))) False) 9.03/9.21 Clause #61 (by superposition #[60, 14]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (imp a a_1) (imp a a))) True) (Eq False True) 9.03/9.21 Clause #67 (by superposition #[60, 44]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp (imp a (imp (nt a_1) (nt a_2))) (imp a (imp a_2 a_1)))) True) (Eq False True) 9.03/9.21 Clause #70 (by superposition #[60, 57]): ∀ (a a_1 a_2 : Iota), 9.03/9.21 Or (Eq (cT (imp (imp (imp a (imp a_1 a_2)) (imp a a_1)) (imp (imp a (imp a_1 a_2)) (imp a a_2)))) True) 9.03/9.21 (Eq False True) 9.03/9.21 Clause #71 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (cT (imp (imp a a_1) (imp a a))) True 9.03/9.21 Clause #72 (by superposition #[71, 10]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a)) True) (Or (Eq True False) (Eq (cT (imp a a_1)) False)) 9.03/9.21 Clause #75 (by clausification #[72]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a)) True) (Eq (cT (imp a a_1)) False) 9.03/9.21 Clause #76 (by superposition #[75, 14]): ∀ (a : Iota), Or (Eq (cT (imp a a)) True) (Eq False True) 9.03/9.21 Clause #80 (by clausification #[76]): ∀ (a : Iota), Eq (cT (imp a a)) True 9.03/9.21 Clause #83 (by superposition #[80, 60]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (imp (imp a a_1) a) (imp (imp a a_1) a_1))) True) (Eq True False) 9.03/9.21 Clause #84 (by superposition #[80, 16]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a (imp a_1 a_1))) True) (Eq True False) 9.03/9.21 Clause #87 (by clausification #[84]): ∀ (a a_1 : Iota), Eq (cT (imp a (imp a_1 a_1))) True 9.03/9.21 Clause #90 (by superposition #[87, 16]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp a (imp a_1 (imp a_2 a_2)))) True) (Eq True False) 9.03/9.21 Clause #92 (by clausification #[90]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp a (imp a_1 (imp a_2 a_2)))) True 9.03/9.21 Clause #215 (by clausification #[83]): ∀ (a a_1 : Iota), Eq (cT (imp (imp (imp a a_1) a) (imp (imp a a_1) a_1))) True 9.03/9.21 Clause #216 (by superposition #[215, 10]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (imp a a_1) a_1)) True) (Or (Eq True False) (Eq (cT (imp (imp a a_1) a)) False)) 9.03/9.21 Clause #279 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp a (imp (nt a_1) (nt a_2))) (imp a (imp a_2 a_1)))) True 9.03/9.21 Clause #304 (by clausification #[216]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (imp a a_1) a_1)) True) (Eq (cT (imp (imp a a_1) a)) False) 9.03/9.21 Clause #305 (by superposition #[304, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp (imp (imp a (imp a_1 a)) a_2) a_2)) True) (Eq False True) 9.03/9.21 Clause #313 (by superposition #[304, 92]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp (imp (imp a (imp a_1 a_1)) a_2) a_2)) True) (Eq False True) 9.03/9.23 Clause #356 (by clausification #[305]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp (imp a (imp a_1 a)) a_2) a_2)) True 9.03/9.23 Clause #357 (by superposition #[356, 10]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT a) True) (Or (Eq True False) (Eq (cT (imp (imp a_1 (imp a_2 a_1)) a)) False)) 9.03/9.23 Clause #367 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp (imp a (imp a_1 a_2)) (imp a a_1)) (imp (imp a (imp a_1 a_2)) (imp a a_2)))) True 9.03/9.23 Clause #377 (by clausification #[313]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp (imp a (imp a_1 a_1)) a_2) a_2)) True 9.03/9.23 Clause #378 (by superposition #[377, 10]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT a) True) (Or (Eq True False) (Eq (cT (imp (imp a_1 (imp a_2 a_2)) a)) False)) 9.03/9.23 Clause #387 (by clausification #[357]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT a) True) (Eq (cT (imp (imp a_1 (imp a_2 a_1)) a)) False) 9.03/9.23 Clause #388 (by superposition #[387, 279]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (nt a) (imp a a_1))) True) (Eq False True) 9.03/9.23 Clause #389 (by clausification #[388]): ∀ (a a_1 : Iota), Eq (cT (imp (nt a) (imp a a_1))) True 9.03/9.23 Clause #395 (by superposition #[389, 16]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp a (imp (nt a_1) (imp a_1 a_2)))) True) (Eq True False) 9.03/9.23 Clause #409 (by clausification #[395]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp a (imp (nt a_1) (imp a_1 a_2)))) True 9.03/9.23 Clause #412 (by superposition #[409, 304]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp (imp (imp (nt a) (imp a a_1)) a_2) a_2)) True) (Eq True False) 9.03/9.23 Clause #605 (by clausification #[378]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT a) True) (Eq (cT (imp (imp a_1 (imp a_2 a_2)) a)) False) 9.03/9.23 Clause #607 (by superposition #[605, 367]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (imp a (imp a a_1)) (imp a a_1))) True) (Eq False True) 9.03/9.23 Clause #609 (by clausification #[607]): ∀ (a a_1 : Iota), Eq (cT (imp (imp a (imp a a_1)) (imp a a_1))) True 9.03/9.23 Clause #610 (by superposition #[609, 10]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a_1)) True) (Or (Eq True False) (Eq (cT (imp a (imp a a_1))) False)) 9.03/9.23 Clause #642 (by clausification #[610]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a_1)) True) (Eq (cT (imp a (imp a a_1))) False) 9.03/9.23 Clause #658 (by clausification #[412]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp (imp (nt a) (imp a a_1)) a_2) a_2)) True 9.03/9.23 Clause #659 (by superposition #[658, 10]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT a) True) (Or (Eq True False) (Eq (cT (imp (imp (nt a_1) (imp a_1 a_2)) a)) False)) 9.03/9.23 Clause #1094 (by clausification #[659]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT a) True) (Eq (cT (imp (imp (nt a_1) (imp a_1 a_2)) a)) False) 9.03/9.23 Clause #1101 (by superposition #[1094, 279]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (nt (nt a)) (imp a_1 a))) True) (Eq False True) 9.03/9.23 Clause #1105 (by clausification #[1101]): ∀ (a a_1 : Iota), Eq (cT (imp (nt (nt a)) (imp a_1 a))) True 9.03/9.23 Clause #1111 (by superposition #[1105, 642]): ∀ (a : Iota), Or (Eq (cT (imp (nt (nt a)) a)) True) (Eq True False) 9.03/9.23 Clause #1116 (by clausification #[1111]): ∀ (a : Iota), Eq (cT (imp (nt (nt a)) a)) True 9.03/9.23 Clause #1118 (by superposition #[1116, 25]): Eq True False 9.03/9.23 Clause #1129 (by clausification #[1118]): False 9.03/9.23 SZS output end Proof for theBenchmark.p 9.03/9.23 EOF