%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GRP700+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 07:49:56 PM UTC 2025 % Result : Theorem 18.59s 18.78s % Output : Proof 18.64s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : GRP700+1 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.13 % Command : duper %s % 0.13/0.34 % Computer : n014.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 17:40:53 EDT 2025 % 0.13/0.34 % CPUTime : % 18.59/18.78 SZS status Theorem for theBenchmark.p % 18.59/18.78 SZS output start Proof for theBenchmark.p % 18.59/18.78 Clause #0 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (ld A B)) B) True % 18.59/18.78 Clause #1 (by assumption #[]): Eq (∀ (B A : Iota), Eq (ld A (mult A B)) B) True % 18.59/18.78 Clause #2 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult (rd A B) B) A) True % 18.59/18.78 Clause #3 (by assumption #[]): Eq (∀ (B A : Iota), Eq (rd (mult A B) B) A) True % 18.59/18.78 Clause #4 (by assumption #[]): Eq (∀ (A : Iota), Eq (mult A unit) A) True % 18.59/18.78 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Eq (mult unit A) A) True % 18.59/18.78 Clause #6 (by assumption #[]): Eq (∀ (C B A : Iota), Eq (mult (mult (mult A B) A) (mult A C)) (mult A (mult (mult (mult B A) A) C))) True % 18.59/18.78 Clause #8 (by assumption #[]): Eq (Not (∀ (X0 : Iota), Exists fun X1 => And (Eq (mult X1 X0) unit) (Eq (mult X0 X1) unit))) True % 18.59/18.78 Clause #9 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (mult unit a) a) True % 18.59/18.78 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (mult unit a) a % 18.59/18.78 Clause #11 (by clausification #[4]): ∀ (a : Iota), Eq (Eq (mult a unit) a) True % 18.59/18.78 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (mult a unit) a % 18.59/18.78 Clause #13 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (rd (mult A a) a) A) True % 18.59/18.78 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Eq (rd (mult a a_1) a_1) a) True % 18.59/18.78 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (rd (mult a a_1) a_1) a % 18.59/18.78 Clause #17 (by superposition #[15, 10]): ∀ (a : Iota), Eq (rd a a) unit % 18.59/18.78 Clause #18 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (ld A a)) a) True % 18.59/18.78 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Eq (mult a (ld a a_1)) a_1) True % 18.59/18.78 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (mult a (ld a a_1)) a_1 % 18.59/18.78 Clause #23 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult (rd A a) a) A) True % 18.59/18.78 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Eq (mult (rd a a_1) a_1) a) True % 18.59/18.78 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (mult (rd a a_1) a_1) a % 18.59/18.78 Clause #27 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (ld A (mult A a)) a) True % 18.59/18.78 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (Eq (ld a (mult a a_1)) a_1) True % 18.59/18.78 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (ld a (mult a a_1)) a_1 % 18.59/18.78 Clause #32 (by superposition #[29, 25]): ∀ (a a_1 : Iota), Eq (ld (rd a a_1) a) a_1 % 18.59/18.78 Clause #33 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B A : Iota), Eq (mult (mult (mult A B) A) (mult A a)) (mult A (mult (mult (mult B A) A) a))) True % 18.59/18.78 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 18.59/18.78 Eq (∀ (A : Iota), Eq (mult (mult (mult A a) A) (mult A a_1)) (mult A (mult (mult (mult a A) A) a_1))) True % 18.59/18.78 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota), Eq (Eq (mult (mult (mult a a_1) a) (mult a a_2)) (mult a (mult (mult (mult a_1 a) a) a_2))) True % 18.59/18.78 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota), Eq (mult (mult (mult a a_1) a) (mult a a_2)) (mult a (mult (mult (mult a_1 a) a) a_2)) % 18.59/18.78 Clause #42 (by superposition #[36, 12]): ∀ (a a_1 : Iota), Eq (mult (mult (mult a a_1) a) a) (mult a (mult (mult (mult a_1 a) a) unit)) % 18.59/18.78 Clause #110 (by clausification #[8]): Eq (∀ (X0 : Iota), Exists fun X1 => And (Eq (mult X1 X0) unit) (Eq (mult X0 X1) unit)) False % 18.59/18.78 Clause #111 (by clausification #[110]): ∀ (a : Iota), Eq (Not (Exists fun X1 => And (Eq (mult X1 (skS.0 0 a)) unit) (Eq (mult (skS.0 0 a) X1) unit))) True % 18.59/18.78 Clause #112 (by clausification #[111]): ∀ (a : Iota), Eq (Exists fun X1 => And (Eq (mult X1 (skS.0 0 a)) unit) (Eq (mult (skS.0 0 a) X1) unit)) False % 18.59/18.78 Clause #113 (by clausification #[112]): ∀ (a a_1 : Iota), Eq (And (Eq (mult a (skS.0 0 a_1)) unit) (Eq (mult (skS.0 0 a_1) a) unit)) False % 18.59/18.78 Clause #114 (by clausification #[113]): ∀ (a a_1 : Iota), Or (Eq (Eq (mult a (skS.0 0 a_1)) unit) False) (Eq (Eq (mult (skS.0 0 a_1) a) unit) False) % 18.59/18.78 Clause #115 (by clausification #[114]): ∀ (a a_1 : Iota), Or (Eq (Eq (mult (skS.0 0 a) a_1) unit) False) (Ne (mult a_1 (skS.0 0 a)) unit) % 18.59/18.78 Clause #116 (by clausification #[115]): ∀ (a a_1 : Iota), Or (Ne (mult a (skS.0 0 a_1)) unit) (Ne (mult (skS.0 0 a_1) a) unit) % 18.64/18.83 Clause #118 (by superposition #[116, 25]): ∀ (a a_1 : Iota), Or (Ne a unit) (Ne (mult (skS.0 0 a_1) (rd a (skS.0 0 a_1))) unit) % 18.64/18.83 Clause #440 (by forward demodulation #[42, 12]): ∀ (a a_1 : Iota), Eq (mult (mult (mult a a_1) a) a) (mult a (mult (mult a_1 a) a)) % 18.64/18.83 Clause #486 (by superposition #[440, 20]): ∀ (a a_1 : Iota), Eq (mult (mult a a_1) a_1) (mult a_1 (mult (mult (ld a_1 a) a_1) a_1)) % 18.64/18.83 Clause #2490 (by superposition #[486, 29]): ∀ (a a_1 : Iota), Eq (ld a (mult (mult a_1 a) a)) (mult (mult (ld a a_1) a) a) % 18.64/18.83 Clause #2794 (by superposition #[2490, 10]): ∀ (a : Iota), Eq (ld a (mult a a)) (mult (mult (ld a unit) a) a) % 18.64/18.83 Clause #2801 (by forward demodulation #[2794, 29]): ∀ (a : Iota), Eq a (mult (mult (ld a unit) a) a) % 18.64/18.83 Clause #2828 (by superposition #[2801, 15]): ∀ (a : Iota), Eq (rd a a) (mult (ld a unit) a) % 18.64/18.83 Clause #3034 (by forward demodulation #[2828, 17]): ∀ (a : Iota), Eq unit (mult (ld a unit) a) % 18.64/18.83 Clause #3092 (by superposition #[3034, 32]): ∀ (a : Iota), Eq unit (mult a (rd unit a)) % 18.64/18.83 Clause #3118 (by superposition #[3092, 29]): ∀ (a : Iota), Eq (ld a unit) (rd unit a) % 18.64/18.83 Clause #5853 (by destructive equality resolution #[118]): ∀ (a : Iota), Ne (mult (skS.0 0 a) (rd unit (skS.0 0 a))) unit % 18.64/18.83 Clause #5854 (by forward demodulation #[5853, 3118]): ∀ (a : Iota), Ne (mult (skS.0 0 a) (ld (skS.0 0 a) unit)) unit % 18.64/18.83 Clause #5855 (by forward demodulation #[5854, 20]): Ne unit unit % 18.64/18.83 Clause #5856 (by eliminate resolved literals #[5855]): False % 18.64/18.83 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------