%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO173^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 08:08:41 PM UTC 2025 % Result : Theorem 6.60s 6.76s % Output : Proof 6.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYO173^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n012.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 : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 13:39:23 EDT 2025 % 0.13/0.35 % CPUTime : % 6.60/6.76 SZS status Theorem for theBenchmark.p % 6.60/6.76 SZS output start Proof for theBenchmark.p % 6.60/6.76 Clause #0 (by assumption #[]): Eq % 6.60/6.76 (Not % 6.60/6.76 (Not % 6.60/6.76 (And % 6.60/6.76 (And % 6.60/6.76 (And % 6.60/6.76 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 6.60/6.76 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) % 6.60/6.76 (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa)))))) % 6.60/6.76 True % 6.60/6.76 Clause #1 (by clausification #[0]): Eq % 6.60/6.76 (Not % 6.60/6.76 (And % 6.60/6.76 (And % 6.60/6.76 (And % 6.60/6.76 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 6.60/6.76 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) % 6.60/6.76 (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa))))) % 6.60/6.76 False % 6.60/6.76 Clause #2 (by clausification #[1]): Eq % 6.60/6.76 (And % 6.60/6.76 (And % 6.60/6.76 (And % 6.60/6.76 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 6.60/6.76 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) % 6.60/6.76 (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa)))) % 6.60/6.76 True % 6.60/6.76 Clause #3 (by clausification #[2]): Eq (Exists fun Xa => Not (cT (imp (nt (nt Xa)) Xa))) True % 6.60/6.76 Clause #4 (by clausification #[2]): Eq % 6.60/6.76 (And % 6.60/6.76 (And % 6.60/6.76 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 6.60/6.76 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp)))) % 6.60/6.76 True % 6.60/6.76 Clause #5 (by clausification #[3]): ∀ (a : Iota), Eq (Not (cT (imp (nt (nt (skS.0 0 a))) (skS.0 0 a)))) True % 6.60/6.76 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (cT (imp (nt (nt (skS.0 0 a))) (skS.0 0 a))) False % 6.60/6.76 Clause #7 (by clausification #[4]): Eq (∀ (Xp Xq : Iota), cT (imp (imp (nt Xp) (nt Xq)) (imp Xq Xp))) True % 6.60/6.76 Clause #8 (by clausification #[4]): Eq % 6.60/6.76 (And % 6.60/6.76 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 6.60/6.76 (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr))))) % 6.60/6.76 True % 6.60/6.76 Clause #9 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Xq : Iota), cT (imp (imp (nt a) (nt Xq)) (imp Xq a))) True % 6.60/6.76 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (cT (imp (imp (nt a) (nt a_1)) (imp a_1 a))) True % 6.60/6.76 Clause #11 (by clausification #[8]): Eq (∀ (Xp Xq Xr : Iota), cT (imp (imp Xp (imp Xq Xr)) (imp (imp Xp Xq) (imp Xp Xr)))) True % 6.60/6.76 Clause #12 (by clausification #[8]): Eq % 6.60/6.76 (And (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) % 6.60/6.76 (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp)))) % 6.60/6.76 True % 6.60/6.76 Clause #13 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Xq Xr : Iota), cT (imp (imp a (imp Xq Xr)) (imp (imp a Xq) (imp a Xr)))) True % 6.60/6.76 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (∀ (Xr : Iota), cT (imp (imp a (imp a_1 Xr)) (imp (imp a a_1) (imp a Xr)))) True % 6.60/6.76 Clause #15 (by clausification #[14]): ∀ (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 % 6.60/6.76 Clause #16 (by clausification #[12]): Eq (∀ (Xp Xq : Iota), cT (imp Xp (imp Xq Xp))) True % 6.60/6.76 Clause #17 (by clausification #[12]): Eq (∀ (Xp Xq : Iota), Or (Or (Not (cT (imp Xp Xq))) (Not (cT Xp))) (cT Xq)) True % 6.60/6.76 Clause #18 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (Xq : Iota), cT (imp a (imp Xq a))) True % 6.60/6.76 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (cT (imp a (imp a_1 a))) True % 6.60/6.76 Clause #20 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (Xq : Iota), Or (Or (Not (cT (imp a Xq))) (Not (cT a))) (cT Xq)) True % 6.60/6.76 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (Or (Or (Not (cT (imp a a_1))) (Not (cT a))) (cT a_1)) True % 6.60/6.79 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (Or (Not (cT (imp a a_1))) (Not (cT a))) True) (Eq (cT a_1) True) % 6.60/6.79 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (cT a) True) (Or (Eq (Not (cT (imp a_1 a))) True) (Eq (Not (cT a_1)) True)) % 6.60/6.79 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (cT a) True) (Or (Eq (Not (cT a_1)) True) (Eq (cT (imp a_1 a)) False)) % 6.60/6.79 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (cT a) True) (Or (Eq (cT (imp a_1 a)) False) (Eq (cT a_1) False)) % 6.60/6.79 Clause #27 (by superposition #[25, 15]): ∀ (a a_1 a_2 : Iota), % 6.60/6.79 Or (Eq (cT (imp (imp a a_1) (imp a a_2))) True) (Or (Eq (cT (imp a (imp a_1 a_2))) False) (Eq False True)) % 6.60/6.79 Clause #28 (by superposition #[25, 19]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a_1)) True) (Or (Eq (cT a_1) False) (Eq False True)) % 6.60/6.79 Clause #30 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a_1)) True) (Eq (cT a_1) False) % 6.60/6.79 Clause #31 (by superposition #[30, 10]): ∀ (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 False True) % 6.60/6.79 Clause #33 (by superposition #[30, 19]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp a (imp a_1 (imp a_2 a_1)))) True) (Eq False True) % 6.60/6.79 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp a (imp a_1 (imp a_2 a_1)))) True % 6.60/6.79 Clause #42 (by clausification #[27]): ∀ (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) % 6.60/6.79 Clause #44 (by superposition #[42, 15]): ∀ (a a_1 a_2 : Iota), % 6.60/6.79 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) % 6.60/6.79 (Eq False True) % 6.60/6.79 Clause #45 (by superposition #[42, 19]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (imp a a_1) (imp a a))) True) (Eq False True) % 6.60/6.79 Clause #48 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (cT (imp (imp a a_1) (imp a a))) True % 6.60/6.79 Clause #49 (by superposition #[48, 25]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a)) True) (Or (Eq True False) (Eq (cT (imp a a_1)) False)) % 6.60/6.79 Clause #52 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a)) True) (Eq (cT (imp a a_1)) False) % 6.60/6.79 Clause #55 (by superposition #[52, 19]): ∀ (a : Iota), Or (Eq (cT (imp a a)) True) (Eq False True) % 6.60/6.79 Clause #57 (by clausification #[55]): ∀ (a : Iota), Eq (cT (imp a a)) True % 6.60/6.79 Clause #60 (by superposition #[57, 42]): ∀ (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) % 6.60/6.79 Clause #61 (by superposition #[57, 30]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a (imp a_1 a_1))) True) (Eq True False) % 6.60/6.79 Clause #63 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp a (imp (imp (nt a_1) (nt a_2)) (imp a_2 a_1)))) True % 6.60/6.79 Clause #65 (by superposition #[63, 42]): ∀ (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 True False) % 6.60/6.79 Clause #67 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (cT (imp a (imp a_1 a_1))) True % 6.60/6.79 Clause #70 (by superposition #[67, 30]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp a (imp a_1 (imp a_2 a_2)))) True) (Eq True False) % 6.60/6.79 Clause #73 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp a (imp a_1 (imp a_2 a_2)))) True % 6.60/6.79 Clause #141 (by clausification #[44]): ∀ (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 % 6.60/6.79 Clause #185 (by clausification #[60]): ∀ (a a_1 : Iota), Eq (cT (imp (imp (imp a a_1) a) (imp (imp a a_1) a_1))) True % 6.60/6.79 Clause #186 (by superposition #[185, 25]): ∀ (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)) % 6.60/6.79 Clause #224 (by clausification #[65]): ∀ (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 % 6.60/6.79 Clause #280 (by clausification #[186]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (imp a a_1) a_1)) True) (Eq (cT (imp (imp a a_1) a)) False) % 6.60/6.79 Clause #281 (by superposition #[280, 34]): ∀ (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) % 6.63/6.81 Clause #285 (by superposition #[280, 73]): ∀ (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) % 6.63/6.81 Clause #329 (by clausification #[281]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp (imp a (imp a_1 a)) a_2) a_2)) True % 6.63/6.81 Clause #330 (by superposition #[329, 25]): ∀ (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)) % 6.63/6.81 Clause #339 (by clausification #[285]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp (imp a (imp a_1 a_1)) a_2) a_2)) True % 6.63/6.81 Clause #340 (by superposition #[339, 25]): ∀ (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)) % 6.63/6.81 Clause #363 (by clausification #[340]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT a) True) (Eq (cT (imp (imp a_1 (imp a_2 a_2)) a)) False) % 6.63/6.81 Clause #365 (by superposition #[363, 141]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (imp a (imp a a_1)) (imp a a_1))) True) (Eq False True) % 6.63/6.81 Clause #367 (by clausification #[365]): ∀ (a a_1 : Iota), Eq (cT (imp (imp a (imp a a_1)) (imp a a_1))) True % 6.63/6.81 Clause #368 (by superposition #[367, 25]): ∀ (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)) % 6.63/6.81 Clause #395 (by clausification #[368]): ∀ (a a_1 : Iota), Or (Eq (cT (imp a a_1)) True) (Eq (cT (imp a (imp a a_1))) False) % 6.63/6.81 Clause #400 (by clausification #[330]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT a) True) (Eq (cT (imp (imp a_1 (imp a_2 a_1)) a)) False) % 6.63/6.81 Clause #401 (by superposition #[400, 224]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (nt a) (imp a a_1))) True) (Eq False True) % 6.63/6.81 Clause #404 (by clausification #[401]): ∀ (a a_1 : Iota), Eq (cT (imp (nt a) (imp a a_1))) True % 6.63/6.81 Clause #409 (by superposition #[404, 30]): ∀ (a a_1 a_2 : Iota), Or (Eq (cT (imp a (imp (nt a_1) (imp a_1 a_2)))) True) (Eq True False) % 6.63/6.81 Clause #414 (by clausification #[409]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp a (imp (nt a_1) (imp a_1 a_2)))) True % 6.63/6.81 Clause #417 (by superposition #[414, 280]): ∀ (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) % 6.63/6.81 Clause #716 (by clausification #[417]): ∀ (a a_1 a_2 : Iota), Eq (cT (imp (imp (imp (nt a) (imp a a_1)) a_2) a_2)) True % 6.63/6.81 Clause #717 (by superposition #[716, 25]): ∀ (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)) % 6.63/6.81 Clause #756 (by clausification #[717]): ∀ (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) % 6.63/6.81 Clause #765 (by superposition #[756, 224]): ∀ (a a_1 : Iota), Or (Eq (cT (imp (nt (nt a)) (imp a_1 a))) True) (Eq False True) % 6.63/6.81 Clause #769 (by clausification #[765]): ∀ (a a_1 : Iota), Eq (cT (imp (nt (nt a)) (imp a_1 a))) True % 6.63/6.81 Clause #774 (by superposition #[769, 395]): ∀ (a : Iota), Or (Eq (cT (imp (nt (nt a)) a)) True) (Eq True False) % 6.63/6.81 Clause #779 (by clausification #[774]): ∀ (a : Iota), Eq (cT (imp (nt (nt a)) a)) True % 6.63/6.81 Clause #780 (by superposition #[779, 6]): Eq True False % 6.63/6.81 Clause #791 (by clausification #[780]): False % 6.63/6.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------