%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GRP704+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 07:49:57 PM UTC 2025 % Result : Theorem 6.43s 6.64s % Output : Proof 6.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : GRP704+1 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.12 % Command : duper %s % 0.12/0.33 % Computer : n014.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Oct 2 17:48:23 EDT 2025 % 0.12/0.33 % CPUTime : % 6.43/6.64 SZS status Theorem for theBenchmark.p % 6.43/6.64 SZS output start Proof for theBenchmark.p % 6.43/6.64 Clause #0 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (ld A B)) B) True % 6.43/6.64 Clause #1 (by assumption #[]): Eq (∀ (B A : Iota), Eq (ld A (mult A B)) B) True % 6.43/6.64 Clause #4 (by assumption #[]): Eq (∀ (A : Iota), Eq (mult A unit) A) True % 6.43/6.64 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Eq (mult unit A) A) True % 6.43/6.64 Clause #7 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult op_c (mult A B)) (mult (mult op_c A) B)) True % 6.43/6.64 Clause #8 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (mult B op_c)) (mult (mult A B) op_c)) True % 6.43/6.64 Clause #9 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (mult op_c B)) (mult (mult A op_c) B)) True % 6.43/6.64 Clause #10 (by assumption #[]): Eq (∀ (A : Iota), Eq op_d (ld A (mult op_c A))) True % 6.43/6.64 Clause #12 (by assumption #[]): Eq (∀ (B A : Iota), Eq op_f (mult A (mult B (ld (mult A B) op_c)))) True % 6.43/6.64 Clause #13 (by assumption #[]): Eq % 6.43/6.64 (Not % 6.43/6.64 (∀ (X4 X5 : Iota), % 6.43/6.64 And % 6.43/6.64 (And (Eq (mult op_f (mult X4 X5)) (mult (mult op_f X4) X5)) % 6.43/6.64 (Eq (mult X4 (mult X5 op_f)) (mult (mult X4 X5) op_f))) % 6.43/6.64 (Eq (mult X4 (mult op_f X5)) (mult (mult X4 op_f) X5)))) % 6.43/6.64 True % 6.43/6.64 Clause #14 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (mult unit a) a) True % 6.43/6.64 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (mult unit a) a % 6.43/6.64 Clause #16 (by clausification #[4]): ∀ (a : Iota), Eq (Eq (mult a unit) a) True % 6.43/6.64 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (mult a unit) a % 6.43/6.64 Clause #18 (by clausification #[10]): ∀ (a : Iota), Eq (Eq op_d (ld a (mult op_c a))) True % 6.43/6.64 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq op_d (ld a (mult op_c a)) % 6.43/6.64 Clause #20 (by superposition #[19, 17]): Eq op_d (ld unit op_c) % 6.43/6.64 Clause #26 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (ld A a)) a) True % 6.43/6.64 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Eq (mult a (ld a a_1)) a_1) True % 6.43/6.64 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (mult a (ld a a_1)) a_1 % 6.43/6.64 Clause #30 (by superposition #[28, 19]): ∀ (a : Iota), Eq op_d (ld (ld op_c a) a) % 6.43/6.64 Clause #32 (by superposition #[28, 20]): Eq (mult unit op_d) op_c % 6.43/6.64 Clause #34 (by superposition #[32, 15]): Eq op_c op_d % 6.43/6.64 Clause #40 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (ld A (mult A a)) a) True % 6.43/6.64 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (Eq (ld a (mult a a_1)) a_1) True % 6.43/6.64 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (ld a (mult a a_1)) a_1 % 6.43/6.64 Clause #50 (by forward demodulation #[30, 34]): ∀ (a : Iota), Eq op_c (ld (ld op_c a) a) % 6.43/6.64 Clause #51 (by superposition #[50, 28]): ∀ (a : Iota), Eq (mult (ld op_c a) op_c) a % 6.43/6.64 Clause #76 (by superposition #[51, 42]): ∀ (a : Iota), Eq (mult a op_c) (mult op_c a) % 6.43/6.64 Clause #87 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult op_c (mult A a)) (mult (mult op_c A) a)) True % 6.43/6.64 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), Eq (Eq (mult op_c (mult a a_1)) (mult (mult op_c a) a_1)) True % 6.43/6.64 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (mult op_c (mult a a_1)) (mult (mult op_c a) a_1) % 6.43/6.64 Clause #105 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (mult a op_c)) (mult (mult A a) op_c)) True % 6.43/6.64 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota), Eq (Eq (mult a (mult a_1 op_c)) (mult (mult a a_1) op_c)) True % 6.43/6.64 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), Eq (mult a (mult a_1 op_c)) (mult (mult a a_1) op_c) % 6.43/6.64 Clause #125 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (mult op_c a)) (mult (mult A op_c) a)) True % 6.43/6.64 Clause #126 (by clausification #[125]): ∀ (a a_1 : Iota), Eq (Eq (mult a (mult op_c a_1)) (mult (mult a op_c) a_1)) True % 6.43/6.64 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), Eq (mult a (mult op_c a_1)) (mult (mult a op_c) a_1) % 6.43/6.64 Clause #185 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq op_f (mult A (mult a (ld (mult A a) op_c)))) True % 6.43/6.64 Clause #186 (by clausification #[185]): ∀ (a a_1 : Iota), Eq (Eq op_f (mult a (mult a_1 (ld (mult a a_1) op_c)))) True % 6.53/6.70 Clause #187 (by clausification #[186]): ∀ (a a_1 : Iota), Eq op_f (mult a (mult a_1 (ld (mult a a_1) op_c))) % 6.53/6.70 Clause #210 (by superposition #[187, 15]): ∀ (a : Iota), Eq op_f (mult unit (mult a (ld a op_c))) % 6.53/6.70 Clause #217 (by forward demodulation #[210, 28]): Eq op_f (mult unit op_c) % 6.53/6.70 Clause #222 (by superposition #[217, 15]): Eq op_f op_c % 6.53/6.70 Clause #230 (by clausification #[13]): Eq % 6.53/6.70 (∀ (X4 X5 : Iota), % 6.53/6.70 And % 6.53/6.70 (And (Eq (mult op_f (mult X4 X5)) (mult (mult op_f X4) X5)) % 6.53/6.70 (Eq (mult X4 (mult X5 op_f)) (mult (mult X4 X5) op_f))) % 6.53/6.70 (Eq (mult X4 (mult op_f X5)) (mult (mult X4 op_f) X5))) % 6.53/6.70 False % 6.53/6.70 Clause #231 (by clausification #[230]): ∀ (a : Iota), % 6.53/6.70 Eq % 6.53/6.70 (Not % 6.53/6.70 (∀ (X5 : Iota), % 6.53/6.70 And % 6.53/6.70 (And (Eq (mult op_f (mult (skS.0 0 a) X5)) (mult (mult op_f (skS.0 0 a)) X5)) % 6.53/6.70 (Eq (mult (skS.0 0 a) (mult X5 op_f)) (mult (mult (skS.0 0 a) X5) op_f))) % 6.53/6.70 (Eq (mult (skS.0 0 a) (mult op_f X5)) (mult (mult (skS.0 0 a) op_f) X5)))) % 6.53/6.70 True % 6.53/6.70 Clause #232 (by clausification #[231]): ∀ (a : Iota), % 6.53/6.70 Eq % 6.53/6.70 (∀ (X5 : Iota), % 6.53/6.70 And % 6.53/6.70 (And (Eq (mult op_f (mult (skS.0 0 a) X5)) (mult (mult op_f (skS.0 0 a)) X5)) % 6.53/6.70 (Eq (mult (skS.0 0 a) (mult X5 op_f)) (mult (mult (skS.0 0 a) X5) op_f))) % 6.53/6.70 (Eq (mult (skS.0 0 a) (mult op_f X5)) (mult (mult (skS.0 0 a) op_f) X5))) % 6.53/6.70 False % 6.53/6.70 Clause #233 (by clausification #[232]): ∀ (a a_1 : Iota), % 6.53/6.70 Eq % 6.53/6.70 (Not % 6.53/6.70 (And % 6.53/6.70 (And (Eq (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) % 6.53/6.70 (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f))) % 6.53/6.70 (Eq (mult (skS.0 0 a) (mult op_f (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_f) (skS.0 1 a a_1))))) % 6.53/6.70 True % 6.53/6.70 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota), % 6.53/6.70 Eq % 6.53/6.70 (And % 6.53/6.70 (And (Eq (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) % 6.53/6.70 (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f))) % 6.53/6.70 (Eq (mult (skS.0 0 a) (mult op_f (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_f) (skS.0 1 a a_1)))) % 6.53/6.70 False % 6.53/6.70 Clause #235 (by clausification #[234]): ∀ (a a_1 : Iota), % 6.53/6.70 Or % 6.53/6.70 (Eq % 6.53/6.70 (And (Eq (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) % 6.53/6.70 (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f))) % 6.53/6.70 False) % 6.53/6.70 (Eq (Eq (mult (skS.0 0 a) (mult op_f (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_f) (skS.0 1 a a_1))) False) % 6.53/6.70 Clause #236 (by clausification #[235]): ∀ (a a_1 : Iota), % 6.53/6.70 Or (Eq (Eq (mult (skS.0 0 a) (mult op_f (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_f) (skS.0 1 a a_1))) False) % 6.53/6.70 (Or (Eq (Eq (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) False) % 6.53/6.70 (Eq (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f)) False)) % 6.53/6.70 Clause #237 (by clausification #[236]): ∀ (a a_1 : Iota), % 6.53/6.70 Or (Eq (Eq (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) False) % 6.53/6.70 (Or (Eq (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f)) False) % 6.53/6.70 (Ne (mult (skS.0 0 a) (mult op_f (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_f) (skS.0 1 a a_1)))) % 6.53/6.70 Clause #238 (by clausification #[237]): ∀ (a a_1 : Iota), % 6.53/6.70 Or (Eq (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f)) False) % 6.53/6.70 (Or (Ne (mult (skS.0 0 a) (mult op_f (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_f) (skS.0 1 a a_1))) % 6.53/6.70 (Ne (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1)))) % 6.53/6.70 Clause #239 (by clausification #[238]): ∀ (a a_1 : Iota), % 6.53/6.70 Or (Ne (mult (skS.0 0 a) (mult op_f (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_f) (skS.0 1 a a_1))) % 6.53/6.70 (Or (Ne (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) % 6.53/6.70 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f))) % 6.55/6.75 Clause #240 (by forward demodulation #[239, 222]): ∀ (a a_1 : Iota), % 6.55/6.75 Or (Ne (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_f) (skS.0 1 a a_1))) % 6.55/6.75 (Or (Ne (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) % 6.55/6.75 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f))) % 6.55/6.75 Clause #241 (by forward demodulation #[240, 222]): ∀ (a a_1 : Iota), % 6.55/6.75 Or (Ne (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_c) (skS.0 1 a a_1))) % 6.55/6.75 (Or (Ne (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) % 6.55/6.75 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f))) % 6.55/6.75 Clause #242 (by forward demodulation #[241, 127]): ∀ (a a_1 : Iota), % 6.55/6.75 Or (Ne (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1))) (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1)))) % 6.55/6.75 (Or (Ne (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) % 6.55/6.75 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f))) % 6.55/6.75 Clause #243 (by eliminate resolved literals #[242]): ∀ (a a_1 : Iota), % 6.55/6.75 Or (Ne (mult op_f (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) % 6.55/6.75 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f)) % 6.55/6.75 Clause #244 (by forward demodulation #[243, 222]): ∀ (a a_1 : Iota), % 6.55/6.75 Or (Ne (mult op_c (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_f (skS.0 0 a)) (skS.0 1 a a_1))) % 6.55/6.75 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f)) % 6.55/6.75 Clause #245 (by forward demodulation #[244, 222]): ∀ (a a_1 : Iota), % 6.55/6.75 Or (Ne (mult op_c (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_c (skS.0 0 a)) (skS.0 1 a a_1))) % 6.55/6.75 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f)) % 6.55/6.75 Clause #246 (by forward demodulation #[245, 89]): ∀ (a a_1 : Iota), % 6.55/6.75 Or (Ne (mult op_c (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult op_c (mult (skS.0 0 a) (skS.0 1 a a_1)))) % 6.55/6.75 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f)) % 6.55/6.75 Clause #247 (by eliminate resolved literals #[246]): ∀ (a a_1 : Iota), Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_f)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f) % 6.55/6.75 Clause #248 (by forward demodulation #[247, 222]): ∀ (a a_1 : Iota), Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_c)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f) % 6.55/6.75 Clause #249 (by forward demodulation #[248, 76]): ∀ (a a_1 : Iota), Ne (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_f) % 6.55/6.75 Clause #250 (by forward demodulation #[249, 222]): ∀ (a a_1 : Iota), Ne (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_c) % 6.55/6.75 Clause #251 (by forward demodulation #[250, 107]): ∀ (a a_1 : Iota), Ne (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1))) (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_c)) % 6.55/6.75 Clause #252 (by forward demodulation #[251, 76]): ∀ (a a_1 : Iota), Ne (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1))) (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1))) % 6.55/6.75 Clause #253 (by eliminate resolved literals #[252]): False % 6.55/6.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------