%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GRP194+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 07:49:19 PM UTC 2025 % Result : Theorem 24.58s 24.78s % Output : Proof 24.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GRP194+1 : TPTP v9.2.0. Released v2.0.0. % 0.03/0.15 % Command : duper %s % 0.14/0.37 % Computer : n027.cluster.edu % 0.14/0.37 % Model : x86_64 x86_64 % 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.37 % Memory : 8042.1875MB % 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.37 % CPULimit : 300 % 0.14/0.37 % WCLimit : 300 % 0.14/0.37 % DateTime : Thu Oct 2 17:09:38 EDT 2025 % 0.14/0.37 % CPUTime : % 24.58/24.78 SZS status Theorem for theBenchmark.p % 24.58/24.78 SZS output start Proof for theBenchmark.p % 24.58/24.78 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), group_member X f → group_member (phi X) h) True % 24.58/24.78 Clause #3 (by assumption #[]): Eq (∀ (X Y : Iota), And (group_member X f) (group_member Y f) → Eq (multiply h (phi X) (phi Y)) (phi (multiply f X Y))) % 24.58/24.78 True % 24.58/24.78 Clause #4 (by assumption #[]): Eq (∀ (X : Iota), group_member X h → Exists fun Y => And (group_member Y f) (Eq (phi Y) X)) True % 24.58/24.78 Clause #5 (by assumption #[]): Eq % 24.58/24.78 (∀ (G X : Iota), % 24.58/24.78 Iff (left_zero G X) (And (group_member X G) (∀ (Y : Iota), group_member Y G → Eq (multiply G X Y) X))) % 24.58/24.78 True % 24.58/24.78 Clause #6 (by assumption #[]): Eq (left_zero f f_left_zero) True % 24.58/24.78 Clause #7 (by assumption #[]): Eq (Not (left_zero h (phi f_left_zero))) True % 24.58/24.78 Clause #8 (by clausification #[7]): Eq (left_zero h (phi f_left_zero)) False % 24.58/24.78 Clause #9 (by clausification #[2]): ∀ (a : Iota), Eq (group_member a f → group_member (phi a) h) True % 24.58/24.78 Clause #10 (by clausification #[9]): ∀ (a : Iota), Or (Eq (group_member a f) False) (Eq (group_member (phi a) h) True) % 24.58/24.78 Clause #16 (by clausification #[4]): ∀ (a : Iota), Eq (group_member a h → Exists fun Y => And (group_member Y f) (Eq (phi Y) a)) True % 24.58/24.78 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (group_member a h) False) (Eq (Exists fun Y => And (group_member Y f) (Eq (phi Y) a)) True) % 24.58/24.78 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 24.58/24.78 Or (Eq (group_member a h) False) (Eq (And (group_member (skS.0 0 a a_1) f) (Eq (phi (skS.0 0 a a_1)) a)) True) % 24.58/24.78 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (group_member a h) False) (Eq (Eq (phi (skS.0 0 a a_1)) a) True) % 24.58/24.78 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (group_member a h) False) (Eq (group_member (skS.0 0 a a_1) f) True) % 24.58/24.78 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (group_member a h) False) (Eq (phi (skS.0 0 a a_1)) a) % 24.58/24.78 Clause #30 (by clausification #[3]): ∀ (a : Iota), % 24.58/24.78 Eq (∀ (Y : Iota), And (group_member a f) (group_member Y f) → Eq (multiply h (phi a) (phi Y)) (phi (multiply f a Y))) % 24.58/24.78 True % 24.58/24.78 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), % 24.58/24.78 Eq (And (group_member a f) (group_member a_1 f) → Eq (multiply h (phi a) (phi a_1)) (phi (multiply f a a_1))) True % 24.58/24.78 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), % 24.58/24.78 Or (Eq (And (group_member a f) (group_member a_1 f)) False) % 24.58/24.78 (Eq (Eq (multiply h (phi a) (phi a_1)) (phi (multiply f a a_1))) True) % 24.58/24.78 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), % 24.58/24.78 Or (Eq (Eq (multiply h (phi a) (phi a_1)) (phi (multiply f a a_1))) True) % 24.58/24.78 (Or (Eq (group_member a f) False) (Eq (group_member a_1 f) False)) % 24.58/24.78 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 24.58/24.78 Or (Eq (group_member a f) False) % 24.58/24.78 (Or (Eq (group_member a_1 f) False) (Eq (multiply h (phi a) (phi a_1)) (phi (multiply f a a_1)))) % 24.58/24.78 Clause #35 (by clausification #[5]): ∀ (a : Iota), % 24.58/24.78 Eq % 24.58/24.78 (∀ (X : Iota), % 24.58/24.78 Iff (left_zero a X) (And (group_member X a) (∀ (Y : Iota), group_member Y a → Eq (multiply a X Y) X))) % 24.58/24.78 True % 24.58/24.78 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), % 24.58/24.78 Eq (Iff (left_zero a a_1) (And (group_member a_1 a) (∀ (Y : Iota), group_member Y a → Eq (multiply a a_1 Y) a_1))) % 24.58/24.78 True % 24.58/24.78 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 24.58/24.78 Or (Eq (left_zero a a_1) True) % 24.58/24.78 (Eq (And (group_member a_1 a) (∀ (Y : Iota), group_member Y a → Eq (multiply a a_1 Y) a_1)) False) % 24.58/24.78 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), % 24.58/24.78 Or (Eq (left_zero a a_1) False) % 24.58/24.78 (Eq (And (group_member a_1 a) (∀ (Y : Iota), group_member Y a → Eq (multiply a a_1 Y) a_1)) True) % 24.58/24.78 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), % 24.58/24.78 Or (Eq (left_zero a a_1) True) % 24.58/24.78 (Or (Eq (group_member a_1 a) False) (Eq (∀ (Y : Iota), group_member Y a → Eq (multiply a a_1 Y) a_1) False)) % 24.58/24.78 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 24.58/24.78 Or (Eq (left_zero a a_1) True) % 24.58/24.78 (Or (Eq (group_member a_1 a) False) % 24.58/24.78 (Eq (Not (group_member (skS.0 1 a a_1 a_2) a → Eq (multiply a a_1 (skS.0 1 a a_1 a_2)) a_1)) True)) % 24.58/24.80 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 24.58/24.80 Or (Eq (left_zero a a_1) True) % 24.58/24.80 (Or (Eq (group_member a_1 a) False) % 24.58/24.80 (Eq (group_member (skS.0 1 a a_1 a_2) a → Eq (multiply a a_1 (skS.0 1 a a_1 a_2)) a_1) False)) % 24.58/24.80 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 24.58/24.80 Or (Eq (left_zero a a_1) True) (Or (Eq (group_member a_1 a) False) (Eq (group_member (skS.0 1 a a_1 a_2) a) True)) % 24.58/24.80 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 24.58/24.80 Or (Eq (left_zero a a_1) True) % 24.58/24.80 (Or (Eq (group_member a_1 a) False) (Eq (Eq (multiply a a_1 (skS.0 1 a a_1 a_2)) a_1) False)) % 24.58/24.80 Clause #44 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (left_zero a a_1) False) (Eq (∀ (Y : Iota), group_member Y a → Eq (multiply a a_1 Y) a_1) True) % 24.58/24.80 Clause #45 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (left_zero a a_1) False) (Eq (group_member a_1 a) True) % 24.58/24.80 Clause #46 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (left_zero a a_1) False) (Eq (group_member a_2 a → Eq (multiply a a_1 a_2) a_1) True) % 24.58/24.80 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), % 24.58/24.80 Or (Eq (left_zero a a_1) False) (Or (Eq (group_member a_2 a) False) (Eq (Eq (multiply a a_1 a_2) a_1) True)) % 24.58/24.80 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (left_zero a a_1) False) (Or (Eq (group_member a_2 a) False) (Eq (multiply a a_1 a_2) a_1)) % 24.58/24.80 Clause #49 (by superposition #[48, 6]): ∀ (a : Iota), Or (Eq (group_member a f) False) (Or (Eq (multiply f f_left_zero a) f_left_zero) (Eq False True)) % 24.58/24.80 Clause #50 (by superposition #[45, 6]): Or (Eq (group_member f_left_zero f) True) (Eq False True) % 24.58/24.80 Clause #51 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 24.58/24.80 Or (Eq (left_zero a a_1) True) (Or (Eq (group_member a_1 a) False) (Ne (multiply a a_1 (skS.0 1 a a_1 a_2)) a_1)) % 24.58/24.80 Clause #52 (by clausification #[50]): Eq (group_member f_left_zero f) True % 24.58/24.80 Clause #53 (by superposition #[52, 10]): Or (Eq True False) (Eq (group_member (phi f_left_zero) h) True) % 24.58/24.80 Clause #54 (by superposition #[52, 34]): ∀ (a : Iota), % 24.58/24.80 Or (Eq True False) % 24.58/24.80 (Or (Eq (group_member a f) False) (Eq (multiply h (phi f_left_zero) (phi a)) (phi (multiply f f_left_zero a)))) % 24.58/24.80 Clause #59 (by clausification #[53]): Eq (group_member (phi f_left_zero) h) True % 24.58/24.80 Clause #64 (by superposition #[59, 42]): ∀ (a : Iota), % 24.58/24.80 Or (Eq (left_zero h (phi f_left_zero)) True) % 24.58/24.80 (Or (Eq True False) (Eq (group_member (skS.0 1 h (phi f_left_zero) a) h) True)) % 24.58/24.80 Clause #65 (by superposition #[59, 51]): ∀ (a : Iota), % 24.58/24.80 Or (Eq (left_zero h (phi f_left_zero)) True) % 24.58/24.80 (Or (Eq True False) (Ne (multiply h (phi f_left_zero) (skS.0 1 h (phi f_left_zero) a)) (phi f_left_zero))) % 24.58/24.80 Clause #66 (by clausification #[49]): ∀ (a : Iota), Or (Eq (group_member a f) False) (Eq (multiply f f_left_zero a) f_left_zero) % 24.58/24.80 Clause #71 (by clausification #[54]): ∀ (a : Iota), % 24.58/24.80 Or (Eq (group_member a f) False) (Eq (multiply h (phi f_left_zero) (phi a)) (phi (multiply f f_left_zero a))) % 24.58/24.80 Clause #107 (by clausification #[64]): ∀ (a : Iota), Or (Eq (left_zero h (phi f_left_zero)) True) (Eq (group_member (skS.0 1 h (phi f_left_zero) a) h) True) % 24.58/24.80 Clause #108 (by forward demodulation #[107, 8]): ∀ (a : Iota), Or (Eq False True) (Eq (group_member (skS.0 1 h (phi f_left_zero) a) h) True) % 24.58/24.80 Clause #109 (by clausification #[108]): ∀ (a : Iota), Eq (group_member (skS.0 1 h (phi f_left_zero) a) h) True % 24.58/24.80 Clause #110 (by superposition #[109, 21]): ∀ (a a_1 : Iota), % 24.58/24.80 Or (Eq True False) (Eq (phi (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1)) (skS.0 1 h (phi f_left_zero) a)) % 24.58/24.80 Clause #111 (by superposition #[109, 20]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (group_member (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1) f) True) % 24.58/24.80 Clause #165 (by clausification #[65]): ∀ (a : Iota), % 24.58/24.80 Or (Eq (left_zero h (phi f_left_zero)) True) % 24.58/24.80 (Ne (multiply h (phi f_left_zero) (skS.0 1 h (phi f_left_zero) a)) (phi f_left_zero)) % 24.58/24.80 Clause #166 (by forward demodulation #[165, 8]): ∀ (a : Iota), Or (Eq False True) (Ne (multiply h (phi f_left_zero) (skS.0 1 h (phi f_left_zero) a)) (phi f_left_zero)) % 24.58/24.82 Clause #167 (by clausification #[166]): ∀ (a : Iota), Ne (multiply h (phi f_left_zero) (skS.0 1 h (phi f_left_zero) a)) (phi f_left_zero) % 24.58/24.82 Clause #168 (by clausification #[111]): ∀ (a a_1 : Iota), Eq (group_member (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1) f) True % 24.58/24.82 Clause #171 (by superposition #[168, 66]): ∀ (a a_1 : Iota), % 24.58/24.82 Or (Eq True False) (Eq (multiply f f_left_zero (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1)) f_left_zero) % 24.58/24.82 Clause #173 (by superposition #[168, 71]): ∀ (a a_1 : Iota), % 24.58/24.82 Or (Eq True False) % 24.58/24.82 (Eq (multiply h (phi f_left_zero) (phi (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1))) % 24.58/24.82 (phi (multiply f f_left_zero (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1)))) % 24.58/24.82 Clause #264 (by clausification #[171]): ∀ (a a_1 : Iota), Eq (multiply f f_left_zero (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1)) f_left_zero % 24.58/24.82 Clause #544 (by clausification #[110]): ∀ (a a_1 : Iota), Eq (phi (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1)) (skS.0 1 h (phi f_left_zero) a) % 24.58/24.82 Clause #2654 (by clausification #[173]): ∀ (a a_1 : Iota), % 24.58/24.82 Eq (multiply h (phi f_left_zero) (phi (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1))) % 24.58/24.82 (phi (multiply f f_left_zero (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1))) % 24.58/24.82 Clause #2655 (by forward demodulation #[2654, 544]): ∀ (a a_1 : Iota), % 24.58/24.82 Eq (multiply h (phi f_left_zero) (skS.0 1 h (phi f_left_zero) a)) % 24.58/24.82 (phi (multiply f f_left_zero (skS.0 0 (skS.0 1 h (phi f_left_zero) a) a_1))) % 24.58/24.82 Clause #2656 (by forward demodulation #[2655, 264]): ∀ (a : Iota), Eq (multiply h (phi f_left_zero) (skS.0 1 h (phi f_left_zero) a)) (phi f_left_zero) % 24.58/24.82 Clause #2657 (by forward contextual literal cutting #[2656, 167]): False % 24.58/24.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------