%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GRP657+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 07:49:51 PM UTC 2025 % Result : Theorem 68.64s 68.84s % Output : Proof 68.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRP657+1 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n022.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 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 17:11:53 EDT 2025 % 0.13/0.35 % CPUTime : % 68.64/68.84 SZS status Theorem for theBenchmark.p % 68.64/68.84 SZS output start Proof for theBenchmark.p % 68.64/68.84 Clause #0 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (ld A B)) B) True % 68.64/68.84 Clause #1 (by assumption #[]): Eq (∀ (B A : Iota), Eq (ld A (mult A B)) B) True % 68.64/68.84 Clause #2 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult (rd A B) B) A) True % 68.64/68.84 Clause #3 (by assumption #[]): Eq (∀ (B A : Iota), Eq (rd (mult A B) B) A) True % 68.64/68.84 Clause #4 (by assumption #[]): Eq (∀ (C B A : Iota), Eq (mult (mult A B) (mult C A)) (mult A (mult (mult B C) A))) True % 68.64/68.84 Clause #5 (by assumption #[]): Eq (Not (Exists fun X0 => ∀ (X1 : Iota), And (Eq (mult X1 X0) X1) (Eq (mult X0 X1) X1))) True % 68.64/68.84 Clause #6 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (rd (mult A a) a) A) True % 68.64/68.84 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Eq (rd (mult a a_1) a_1) a) True % 68.64/68.84 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (rd (mult a a_1) a_1) a % 68.64/68.84 Clause #9 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult (rd A a) a) A) True % 68.64/68.84 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Eq (mult (rd a a_1) a_1) a) True % 68.64/68.84 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (mult (rd a a_1) a_1) a % 68.64/68.84 Clause #12 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (ld A (mult A a)) a) True % 68.64/68.84 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (Eq (ld a (mult a a_1)) a_1) True % 68.64/68.84 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (ld a (mult a a_1)) a_1 % 68.64/68.84 Clause #16 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (ld A a)) a) True % 68.64/68.84 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (Eq (mult a (ld a a_1)) a_1) True % 68.64/68.84 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (mult a (ld a a_1)) a_1 % 68.64/68.84 Clause #19 (by superposition #[18, 8]): ∀ (a a_1 : Iota), Eq (rd a (ld a_1 a)) a_1 % 68.64/68.84 Clause #20 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B A : Iota), Eq (mult (mult A B) (mult a A)) (mult A (mult (mult B a) A))) True % 68.64/68.84 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (∀ (A : Iota), Eq (mult (mult A a) (mult a_1 A)) (mult A (mult (mult a a_1) A))) True % 68.64/68.84 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Eq (Eq (mult (mult a a_1) (mult a_2 a)) (mult a (mult (mult a_1 a_2) a))) True % 68.64/68.84 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Eq (mult (mult a a_1) (mult a_2 a)) (mult a (mult (mult a_1 a_2) a)) % 68.64/68.84 Clause #25 (by superposition #[23, 14]): ∀ (a a_1 a_2 : Iota), Eq (ld (mult a a_1) (mult a (mult (mult a_1 a_2) a))) (mult a_2 a) % 68.64/68.84 Clause #38 (by superposition #[25, 18]): ∀ (a a_1 a_2 : Iota), Eq (ld a (mult a_1 (mult (mult (ld a_1 a) a_2) a_1))) (mult a_2 a_1) % 68.64/68.84 Clause #40 (by superposition #[38, 14]): ∀ (a a_1 : Iota), Eq (mult a a_1) (mult (mult (ld a_1 a_1) a) a_1) % 68.64/68.84 Clause #52 (by superposition #[40, 18]): ∀ (a a_1 : Iota), Eq (mult (ld (ld a a) a_1) a) (mult a_1 a) % 68.64/68.84 Clause #56 (by superposition #[52, 14]): ∀ (a a_1 : Iota), Eq (ld (ld (ld a a) a_1) (mult a_1 a)) a % 68.64/68.84 Clause #62 (by clausification #[5]): Eq (Exists fun X0 => ∀ (X1 : Iota), And (Eq (mult X1 X0) X1) (Eq (mult X0 X1) X1)) False % 68.64/68.84 Clause #63 (by clausification #[62]): ∀ (a : Iota), Eq (∀ (X1 : Iota), And (Eq (mult X1 a) X1) (Eq (mult a X1) X1)) False % 68.64/68.84 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 68.64/68.84 Eq (Not (And (Eq (mult (skS.0 0 a a_1) a) (skS.0 0 a a_1)) (Eq (mult a (skS.0 0 a a_1)) (skS.0 0 a a_1)))) True % 68.64/68.84 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), % 68.64/68.84 Eq (And (Eq (mult (skS.0 0 a a_1) a) (skS.0 0 a a_1)) (Eq (mult a (skS.0 0 a a_1)) (skS.0 0 a a_1))) False % 68.64/68.84 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 68.64/68.84 Or (Eq (Eq (mult (skS.0 0 a a_1) a) (skS.0 0 a a_1)) False) (Eq (Eq (mult a (skS.0 0 a a_1)) (skS.0 0 a a_1)) False) % 68.64/68.84 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 68.64/68.84 Or (Eq (Eq (mult a (skS.0 0 a a_1)) (skS.0 0 a a_1)) False) (Ne (mult (skS.0 0 a a_1) a) (skS.0 0 a a_1)) % 68.64/68.84 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Or (Ne (mult (skS.0 0 a a_1) a) (skS.0 0 a a_1)) (Ne (mult a (skS.0 0 a a_1)) (skS.0 0 a a_1)) % 68.80/69.00 Clause #72 (by superposition #[56, 11]): ∀ (a a_1 : Iota), Eq (ld (ld (ld a a) (rd a_1 a)) a_1) a % 68.80/69.00 Clause #78 (by superposition #[72, 19]): ∀ (a a_1 : Iota), Eq (rd a a_1) (ld (ld a_1 a_1) (rd a a_1)) % 68.80/69.00 Clause #85 (by superposition #[78, 8]): ∀ (a a_1 : Iota), Eq a (ld (ld a_1 a_1) a) % 68.80/69.00 Clause #89 (by superposition #[85, 19]): ∀ (a a_1 : Iota), Eq (rd a a) (ld a_1 a_1) % 68.80/69.00 Clause #106 (by superposition #[89, 18]): ∀ (a a_1 : Iota), Eq (mult a (rd a_1 a_1)) a % 68.80/69.00 Clause #111 (by superposition #[89, 89]): ∀ (a a_1 : Iota), Eq (rd a a) (rd a_1 a_1) % 68.80/69.00 Clause #112 (by superposition #[111, 11]): ∀ (a a_1 : Iota), Eq (mult (rd a a) a_1) a_1 % 68.80/69.00 Clause #162 (by superposition #[106, 68]): ∀ (a a_1 : Iota), % 68.80/69.00 Or (Ne (skS.0 0 (rd a a) a_1) (skS.0 0 (rd a a) a_1)) % 68.80/69.00 (Ne (mult (rd a a) (skS.0 0 (rd a a) a_1)) (skS.0 0 (rd a a) a_1)) % 68.80/69.00 Clause #20517 (by eliminate resolved literals #[162]): ∀ (a a_1 : Iota), Ne (mult (rd a a) (skS.0 0 (rd a a) a_1)) (skS.0 0 (rd a a) a_1) % 68.80/69.00 Clause #20518 (by forward demodulation #[20517, 112]): ∀ (a a_1 : Iota), Ne (skS.0 0 (rd a a) a_1) (skS.0 0 (rd a a) a_1) % 68.80/69.00 Clause #20519 (by eliminate resolved literals #[20518]): False % 68.80/69.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------