%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GRP702+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 4.08s 4.30s % Output : Proof 4.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP702+1 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n016.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 18:11:08 EDT 2025 % 0.13/0.35 % CPUTime : % 4.08/4.30 SZS status Theorem for theBenchmark.p % 4.08/4.30 SZS output start Proof for theBenchmark.p % 4.08/4.30 Clause #0 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (ld A B)) B) True % 4.08/4.30 Clause #1 (by assumption #[]): Eq (∀ (B A : Iota), Eq (ld A (mult A B)) B) True % 4.08/4.30 Clause #4 (by assumption #[]): Eq (∀ (A : Iota), Eq (mult A unit) A) True % 4.08/4.30 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Eq (mult unit A) A) True % 4.08/4.30 Clause #7 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult op_c (mult A B)) (mult (mult op_c A) B)) True % 4.08/4.30 Clause #8 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (mult B op_c)) (mult (mult A B) op_c)) True % 4.08/4.30 Clause #9 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (mult op_c B)) (mult (mult A op_c) B)) True % 4.08/4.30 Clause #10 (by assumption #[]): Eq (∀ (A : Iota), Eq op_d (ld A (mult op_c A))) True % 4.08/4.30 Clause #13 (by assumption #[]): Eq % 4.08/4.30 (Not % 4.08/4.30 (∀ (X0 X1 : Iota), % 4.08/4.30 And % 4.08/4.30 (And (Eq (mult op_d (mult X0 X1)) (mult (mult op_d X0) X1)) % 4.08/4.30 (Eq (mult X0 (mult X1 op_d)) (mult (mult X0 X1) op_d))) % 4.08/4.30 (Eq (mult X0 (mult op_d X1)) (mult (mult X0 op_d) X1)))) % 4.08/4.30 True % 4.08/4.30 Clause #14 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (mult unit a) a) True % 4.08/4.30 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (mult unit a) a % 4.08/4.30 Clause #16 (by clausification #[4]): ∀ (a : Iota), Eq (Eq (mult a unit) a) True % 4.08/4.30 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (mult a unit) a % 4.08/4.30 Clause #18 (by clausification #[10]): ∀ (a : Iota), Eq (Eq op_d (ld a (mult op_c a))) True % 4.08/4.30 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq op_d (ld a (mult op_c a)) % 4.08/4.30 Clause #20 (by superposition #[19, 17]): Eq op_d (ld unit op_c) % 4.08/4.30 Clause #26 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (ld A a)) a) True % 4.08/4.30 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Eq (mult a (ld a a_1)) a_1) True % 4.08/4.30 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (mult a (ld a a_1)) a_1 % 4.08/4.30 Clause #30 (by superposition #[28, 19]): ∀ (a : Iota), Eq op_d (ld (ld op_c a) a) % 4.08/4.30 Clause #32 (by superposition #[28, 20]): Eq (mult unit op_d) op_c % 4.08/4.30 Clause #34 (by superposition #[32, 15]): Eq op_c op_d % 4.08/4.30 Clause #40 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (ld A (mult A a)) a) True % 4.08/4.30 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (Eq (ld a (mult a a_1)) a_1) True % 4.08/4.30 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (ld a (mult a a_1)) a_1 % 4.08/4.30 Clause #50 (by forward demodulation #[30, 34]): ∀ (a : Iota), Eq op_c (ld (ld op_c a) a) % 4.08/4.30 Clause #51 (by superposition #[50, 28]): ∀ (a : Iota), Eq (mult (ld op_c a) op_c) a % 4.08/4.30 Clause #76 (by superposition #[51, 42]): ∀ (a : Iota), Eq (mult a op_c) (mult op_c a) % 4.08/4.30 Clause #87 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult op_c (mult A a)) (mult (mult op_c A) a)) True % 4.08/4.30 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 % 4.08/4.30 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (mult op_c (mult a a_1)) (mult (mult op_c a) a_1) % 4.08/4.30 Clause #105 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (mult a op_c)) (mult (mult A a) op_c)) True % 4.08/4.30 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 % 4.08/4.30 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), Eq (mult a (mult a_1 op_c)) (mult (mult a a_1) op_c) % 4.08/4.30 Clause #125 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (mult op_c a)) (mult (mult A op_c) a)) True % 4.08/4.30 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 % 4.08/4.30 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), Eq (mult a (mult op_c a_1)) (mult (mult a op_c) a_1) % 4.08/4.30 Clause #230 (by clausification #[13]): Eq % 4.08/4.30 (∀ (X0 X1 : Iota), % 4.08/4.30 And % 4.08/4.30 (And (Eq (mult op_d (mult X0 X1)) (mult (mult op_d X0) X1)) % 4.08/4.30 (Eq (mult X0 (mult X1 op_d)) (mult (mult X0 X1) op_d))) % 4.08/4.30 (Eq (mult X0 (mult op_d X1)) (mult (mult X0 op_d) X1))) % 4.08/4.30 False % 4.08/4.30 Clause #231 (by clausification #[230]): ∀ (a : Iota), % 4.08/4.30 Eq % 4.08/4.32 (Not % 4.08/4.32 (∀ (X1 : Iota), % 4.08/4.32 And % 4.08/4.32 (And (Eq (mult op_d (mult (skS.0 0 a) X1)) (mult (mult op_d (skS.0 0 a)) X1)) % 4.08/4.32 (Eq (mult (skS.0 0 a) (mult X1 op_d)) (mult (mult (skS.0 0 a) X1) op_d))) % 4.08/4.32 (Eq (mult (skS.0 0 a) (mult op_d X1)) (mult (mult (skS.0 0 a) op_d) X1)))) % 4.08/4.32 True % 4.08/4.32 Clause #232 (by clausification #[231]): ∀ (a : Iota), % 4.08/4.32 Eq % 4.08/4.32 (∀ (X1 : Iota), % 4.08/4.32 And % 4.08/4.32 (And (Eq (mult op_d (mult (skS.0 0 a) X1)) (mult (mult op_d (skS.0 0 a)) X1)) % 4.08/4.32 (Eq (mult (skS.0 0 a) (mult X1 op_d)) (mult (mult (skS.0 0 a) X1) op_d))) % 4.08/4.32 (Eq (mult (skS.0 0 a) (mult op_d X1)) (mult (mult (skS.0 0 a) op_d) X1))) % 4.08/4.32 False % 4.08/4.32 Clause #233 (by clausification #[232]): ∀ (a a_1 : Iota), % 4.08/4.32 Eq % 4.08/4.32 (Not % 4.08/4.32 (And % 4.08/4.32 (And (Eq (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) % 4.08/4.32 (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d))) % 4.08/4.32 (Eq (mult (skS.0 0 a) (mult op_d (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_d) (skS.0 1 a a_1))))) % 4.08/4.32 True % 4.08/4.32 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota), % 4.08/4.32 Eq % 4.08/4.32 (And % 4.08/4.32 (And (Eq (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) % 4.08/4.32 (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d))) % 4.08/4.32 (Eq (mult (skS.0 0 a) (mult op_d (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_d) (skS.0 1 a a_1)))) % 4.08/4.32 False % 4.08/4.32 Clause #235 (by clausification #[234]): ∀ (a a_1 : Iota), % 4.08/4.32 Or % 4.08/4.32 (Eq % 4.08/4.32 (And (Eq (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) % 4.08/4.32 (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d))) % 4.08/4.32 False) % 4.08/4.32 (Eq (Eq (mult (skS.0 0 a) (mult op_d (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_d) (skS.0 1 a a_1))) False) % 4.08/4.32 Clause #236 (by clausification #[235]): ∀ (a a_1 : Iota), % 4.08/4.32 Or (Eq (Eq (mult (skS.0 0 a) (mult op_d (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_d) (skS.0 1 a a_1))) False) % 4.08/4.32 (Or (Eq (Eq (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) False) % 4.08/4.32 (Eq (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d)) False)) % 4.08/4.32 Clause #237 (by clausification #[236]): ∀ (a a_1 : Iota), % 4.08/4.32 Or (Eq (Eq (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) False) % 4.08/4.32 (Or (Eq (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d)) False) % 4.08/4.32 (Ne (mult (skS.0 0 a) (mult op_d (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_d) (skS.0 1 a a_1)))) % 4.08/4.32 Clause #238 (by clausification #[237]): ∀ (a a_1 : Iota), % 4.08/4.32 Or (Eq (Eq (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d)) False) % 4.08/4.32 (Or (Ne (mult (skS.0 0 a) (mult op_d (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_d) (skS.0 1 a a_1))) % 4.08/4.32 (Ne (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1)))) % 4.08/4.32 Clause #239 (by clausification #[238]): ∀ (a a_1 : Iota), % 4.08/4.32 Or (Ne (mult (skS.0 0 a) (mult op_d (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_d) (skS.0 1 a a_1))) % 4.08/4.32 (Or (Ne (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) % 4.08/4.32 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d))) % 4.08/4.32 Clause #240 (by forward demodulation #[239, 34]): ∀ (a a_1 : Iota), % 4.08/4.32 Or (Ne (mult (skS.0 0 a) (mult op_c (skS.0 1 a a_1))) (mult (mult (skS.0 0 a) op_d) (skS.0 1 a a_1))) % 4.08/4.32 (Or (Ne (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) % 4.08/4.32 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d))) % 4.08/4.32 Clause #241 (by forward demodulation #[240, 34]): ∀ (a a_1 : Iota), % 4.08/4.32 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))) % 4.08/4.32 (Or (Ne (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) % 4.16/4.34 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d))) % 4.16/4.34 Clause #242 (by forward demodulation #[241, 127]): ∀ (a a_1 : Iota), % 4.16/4.34 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)))) % 4.16/4.34 (Or (Ne (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) % 4.16/4.34 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d))) % 4.16/4.34 Clause #243 (by eliminate resolved literals #[242]): ∀ (a a_1 : Iota), % 4.16/4.34 Or (Ne (mult op_d (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) % 4.16/4.34 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d)) % 4.16/4.34 Clause #244 (by forward demodulation #[243, 34]): ∀ (a a_1 : Iota), % 4.16/4.34 Or (Ne (mult op_c (mult (skS.0 0 a) (skS.0 1 a a_1))) (mult (mult op_d (skS.0 0 a)) (skS.0 1 a a_1))) % 4.16/4.34 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d)) % 4.16/4.34 Clause #245 (by forward demodulation #[244, 34]): ∀ (a a_1 : Iota), % 4.16/4.34 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))) % 4.16/4.34 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d)) % 4.16/4.34 Clause #246 (by forward demodulation #[245, 89]): ∀ (a a_1 : Iota), % 4.16/4.34 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)))) % 4.16/4.34 (Ne (mult (skS.0 0 a) (mult (skS.0 1 a a_1) op_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d)) % 4.16/4.34 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_d)) (mult (mult (skS.0 0 a) (skS.0 1 a a_1)) op_d) % 4.16/4.34 Clause #248 (by forward demodulation #[247, 34]): ∀ (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_d) % 4.16/4.34 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_d) % 4.16/4.34 Clause #250 (by forward demodulation #[249, 34]): ∀ (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) % 4.16/4.34 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)) % 4.16/4.34 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))) % 4.16/4.34 Clause #253 (by eliminate resolved literals #[252]): False % 4.16/4.34 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------