TSTP Solution File: GRP702+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GRP702+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 : Thu Aug 31 00:33:27 EDT 2023
% Result : Theorem 3.98s 4.16s
% Output : Proof 4.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP702+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n023.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 : Mon Aug 28 21:35:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.98/4.16 SZS status Theorem for theBenchmark.p
% 3.98/4.16 SZS output start Proof for theBenchmark.p
% 3.98/4.16 Clause #0 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (ld A B)) B) True
% 3.98/4.16 Clause #1 (by assumption #[]): Eq (∀ (B A : Iota), Eq (ld A (mult A B)) B) True
% 3.98/4.16 Clause #4 (by assumption #[]): Eq (∀ (A : Iota), Eq (mult A unit) A) True
% 3.98/4.16 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Eq (mult unit A) A) True
% 3.98/4.16 Clause #7 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult op_c (mult A B)) (mult (mult op_c A) B)) True
% 3.98/4.16 Clause #8 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (mult B op_c)) (mult (mult A B) op_c)) True
% 3.98/4.16 Clause #9 (by assumption #[]): Eq (∀ (B A : Iota), Eq (mult A (mult op_c B)) (mult (mult A op_c) B)) True
% 3.98/4.16 Clause #10 (by assumption #[]): Eq (∀ (A : Iota), Eq op_d (ld A (mult op_c A))) True
% 3.98/4.16 Clause #13 (by assumption #[]): Eq
% 3.98/4.16 (Not
% 3.98/4.16 (∀ (X0 X1 : Iota),
% 3.98/4.16 And
% 3.98/4.16 (And (Eq (mult op_d (mult X0 X1)) (mult (mult op_d X0) X1))
% 3.98/4.16 (Eq (mult X0 (mult X1 op_d)) (mult (mult X0 X1) op_d)))
% 3.98/4.16 (Eq (mult X0 (mult op_d X1)) (mult (mult X0 op_d) X1))))
% 3.98/4.16 True
% 3.98/4.16 Clause #14 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (mult unit a) a) True
% 3.98/4.16 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (mult unit a) a
% 3.98/4.16 Clause #16 (by clausification #[4]): ∀ (a : Iota), Eq (Eq (mult a unit) a) True
% 3.98/4.16 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (mult a unit) a
% 3.98/4.16 Clause #18 (by clausification #[10]): ∀ (a : Iota), Eq (Eq op_d (ld a (mult op_c a))) True
% 3.98/4.16 Clause #19 (by clausification #[18]): ∀ (a : Iota), Eq op_d (ld a (mult op_c a))
% 3.98/4.16 Clause #20 (by superposition #[19, 17]): Eq op_d (ld unit op_c)
% 3.98/4.16 Clause #26 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (ld A a)) a) True
% 3.98/4.16 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Eq (mult a (ld a a_1)) a_1) True
% 3.98/4.16 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (mult a (ld a a_1)) a_1
% 3.98/4.16 Clause #30 (by superposition #[28, 19]): ∀ (a : Iota), Eq op_d (ld (ld op_c a) a)
% 3.98/4.16 Clause #32 (by superposition #[28, 20]): Eq (mult unit op_d) op_c
% 3.98/4.16 Clause #34 (by superposition #[32, 15]): Eq op_c op_d
% 3.98/4.16 Clause #40 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (ld A (mult A a)) a) True
% 3.98/4.16 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (Eq (ld a (mult a a_1)) a_1) True
% 3.98/4.16 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (ld a (mult a a_1)) a_1
% 3.98/4.16 Clause #50 (by forward demodulation #[30, 34]): ∀ (a : Iota), Eq op_c (ld (ld op_c a) a)
% 3.98/4.16 Clause #51 (by superposition #[50, 28]): ∀ (a : Iota), Eq (mult (ld op_c a) op_c) a
% 3.98/4.16 Clause #76 (by superposition #[51, 42]): ∀ (a : Iota), Eq (mult a op_c) (mult op_c a)
% 3.98/4.16 Clause #87 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult op_c (mult A a)) (mult (mult op_c A) a)) True
% 3.98/4.16 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
% 3.98/4.16 Clause #89 (by clausification #[88]): ∀ (a a_1 : Iota), Eq (mult op_c (mult a a_1)) (mult (mult op_c a) a_1)
% 3.98/4.16 Clause #105 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (mult a op_c)) (mult (mult A a) op_c)) True
% 3.98/4.16 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
% 3.98/4.16 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota), Eq (mult a (mult a_1 op_c)) (mult (mult a a_1) op_c)
% 3.98/4.16 Clause #125 (by clausification #[9]): ∀ (a : Iota), Eq (∀ (A : Iota), Eq (mult A (mult op_c a)) (mult (mult A op_c) a)) True
% 3.98/4.16 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
% 3.98/4.16 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), Eq (mult a (mult op_c a_1)) (mult (mult a op_c) a_1)
% 3.98/4.16 Clause #230 (by clausification #[13]): Eq
% 3.98/4.16 (∀ (X0 X1 : Iota),
% 3.98/4.16 And
% 3.98/4.16 (And (Eq (mult op_d (mult X0 X1)) (mult (mult op_d X0) X1))
% 3.98/4.16 (Eq (mult X0 (mult X1 op_d)) (mult (mult X0 X1) op_d)))
% 3.98/4.16 (Eq (mult X0 (mult op_d X1)) (mult (mult X0 op_d) X1)))
% 3.98/4.16 False
% 3.98/4.16 Clause #231 (by clausification #[230]): ∀ (a : Iota),
% 3.98/4.16 Eq
% 4.02/4.18 (Not
% 4.02/4.18 (∀ (X1 : Iota),
% 4.02/4.18 And
% 4.02/4.18 (And (Eq (mult op_d (mult (skS.0 0 a) X1)) (mult (mult op_d (skS.0 0 a)) X1))
% 4.02/4.18 (Eq (mult (skS.0 0 a) (mult X1 op_d)) (mult (mult (skS.0 0 a) X1) op_d)))
% 4.02/4.18 (Eq (mult (skS.0 0 a) (mult op_d X1)) (mult (mult (skS.0 0 a) op_d) X1))))
% 4.02/4.18 True
% 4.02/4.18 Clause #232 (by clausification #[231]): ∀ (a : Iota),
% 4.02/4.18 Eq
% 4.02/4.18 (∀ (X1 : Iota),
% 4.02/4.18 And
% 4.02/4.18 (And (Eq (mult op_d (mult (skS.0 0 a) X1)) (mult (mult op_d (skS.0 0 a)) X1))
% 4.02/4.18 (Eq (mult (skS.0 0 a) (mult X1 op_d)) (mult (mult (skS.0 0 a) X1) op_d)))
% 4.02/4.18 (Eq (mult (skS.0 0 a) (mult op_d X1)) (mult (mult (skS.0 0 a) op_d) X1)))
% 4.02/4.18 False
% 4.02/4.18 Clause #233 (by clausification #[232]): ∀ (a a_1 : Iota),
% 4.02/4.18 Eq
% 4.02/4.18 (Not
% 4.02/4.18 (And
% 4.02/4.18 (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)))
% 4.02/4.18 (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)))
% 4.02/4.18 (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)))))
% 4.02/4.19 True
% 4.02/4.19 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota),
% 4.02/4.19 Eq
% 4.02/4.19 (And
% 4.02/4.19 (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)))
% 4.02/4.19 (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)))
% 4.02/4.19 (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))))
% 4.02/4.19 False
% 4.02/4.19 Clause #235 (by clausification #[234]): ∀ (a a_1 : Iota),
% 4.02/4.19 Or
% 4.02/4.19 (Eq
% 4.02/4.19 (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)))
% 4.02/4.19 (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)))
% 4.02/4.19 False)
% 4.02/4.19 (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)
% 4.02/4.19 Clause #236 (by clausification #[235]): ∀ (a a_1 : Iota),
% 4.02/4.19 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)
% 4.02/4.19 (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)
% 4.02/4.19 (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))
% 4.02/4.19 Clause #237 (by clausification #[236]): ∀ (a a_1 : Iota),
% 4.02/4.19 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)
% 4.02/4.19 (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)
% 4.02/4.19 (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))))
% 4.02/4.19 Clause #238 (by clausification #[237]): ∀ (a a_1 : Iota),
% 4.02/4.19 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)
% 4.02/4.19 (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)))
% 4.02/4.19 (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))))
% 4.02/4.19 Clause #239 (by clausification #[238]): ∀ (a a_1 : Iota),
% 4.02/4.19 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)))
% 4.02/4.19 (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)))
% 4.02/4.19 (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)))
% 4.02/4.19 Clause #240 (by forward demodulation #[239, 34]): ∀ (a a_1 : Iota),
% 4.02/4.19 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)))
% 4.02/4.19 (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)))
% 4.02/4.19 (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)))
% 4.02/4.19 Clause #241 (by forward demodulation #[240, 34]): ∀ (a a_1 : Iota),
% 4.02/4.19 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)))
% 4.02/4.19 (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)))
% 4.02/4.20 (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)))
% 4.02/4.20 Clause #242 (by forward demodulation #[241, 127]): ∀ (a a_1 : Iota),
% 4.02/4.20 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))))
% 4.02/4.20 (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)))
% 4.02/4.20 (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)))
% 4.02/4.20 Clause #243 (by eliminate resolved literals #[242]): ∀ (a a_1 : Iota),
% 4.02/4.20 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)))
% 4.02/4.20 (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))
% 4.02/4.20 Clause #244 (by forward demodulation #[243, 34]): ∀ (a a_1 : Iota),
% 4.02/4.20 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)))
% 4.02/4.20 (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))
% 4.02/4.20 Clause #245 (by forward demodulation #[244, 34]): ∀ (a a_1 : Iota),
% 4.02/4.20 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)))
% 4.02/4.20 (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))
% 4.02/4.20 Clause #246 (by forward demodulation #[245, 89]): ∀ (a a_1 : Iota),
% 4.02/4.20 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))))
% 4.02/4.20 (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))
% 4.02/4.20 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)
% 4.02/4.20 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)
% 4.02/4.20 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)
% 4.02/4.20 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)
% 4.02/4.20 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))
% 4.02/4.20 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)))
% 4.02/4.20 Clause #253 (by eliminate resolved literals #[252]): False
% 4.02/4.20 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------