TSTP Solution File: NUM483+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM483+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %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 : 600s
% DateTime : Mon Jul 18 14:26:40 EDT 2022
% Result : Theorem 0.68s 0.85s
% Output : Refutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 27
% Syntax : Number of clauses : 94 ( 38 unt; 17 nHn; 94 RR)
% Number of literals : 225 ( 0 equ; 114 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM483+3.p',unknown),
[] ).
cnf(2,axiom,
aNaturalNumber0(sz10),
file('NUM483+3.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xk),
file('NUM483+3.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(skc3),
file('NUM483+3.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(skc2),
file('NUM483+3.p',unknown),
[] ).
cnf(10,axiom,
aNaturalNumber0(skf12(u)),
file('NUM483+3.p',unknown),
[] ).
cnf(11,axiom,
doDivides0(skc2,xk),
file('NUM483+3.p',unknown),
[] ).
cnf(15,axiom,
aNaturalNumber0(skf10(u,v)),
file('NUM483+3.p',unknown),
[] ).
cnf(16,axiom,
~ equal(xk,sz00),
file('NUM483+3.p',unknown),
[] ).
cnf(18,axiom,
~ equal(skc2,sz10),
file('NUM483+3.p',unknown),
[] ).
cnf(19,axiom,
~ equal(skc2,xk),
file('NUM483+3.p',unknown),
[] ).
cnf(20,axiom,
equal(sdtasdt0(skc2,skc3),xk),
file('NUM483+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ doDivides0(u,xk)
| skP0(u) ),
file('NUM483+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM483+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(sz10,u),u) ),
file('NUM483+3.p',unknown),
[] ).
cnf(28,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(sz00,u),sz00) ),
file('NUM483+3.p',unknown),
[] ).
cnf(29,axiom,
( ~ skP0(u)
| ~ aNaturalNumber0(u)
| ~ isPrime0(u) ),
file('NUM483+3.p',unknown),
[] ).
cnf(34,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(v,u),xk)
| skP0(v) ),
file('NUM483+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM483+3.p',unknown),
[] ).
cnf(41,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(v,sz00)
| sdtlseqdt0(u,sdtasdt0(u,v)) ),
file('NUM483+3.p',unknown),
[] ).
cnf(45,axiom,
( ~ skP0(u)
| ~ aNaturalNumber0(u)
| equal(u,sz10)
| equal(u,sz00)
| doDivides0(skf7(u),u) ),
file('NUM483+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| iLess0(v,u)
| equal(v,u) ),
file('NUM483+3.p',unknown),
[] ).
cnf(50,axiom,
( ~ aNaturalNumber0(u)
| ~ iLess0(u,xk)
| isPrime0(skf12(u))
| equal(u,sz10)
| equal(u,sz00) ),
file('NUM483+3.p',unknown),
[] ).
cnf(55,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| equal(sdtasdt0(v,skf10(v,u)),u) ),
file('NUM483+3.p',unknown),
[] ).
cnf(56,axiom,
( ~ aNaturalNumber0(u)
| ~ iLess0(u,xk)
| equal(u,sz10)
| equal(u,sz00)
| doDivides0(skf12(u),u) ),
file('NUM483+3.p',unknown),
[] ).
cnf(66,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,u)
| ~ doDivides0(w,v)
| doDivides0(w,u) ),
file('NUM483+3.p',unknown),
[] ).
cnf(70,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('NUM483+3.p',unknown),
[] ).
cnf(362,plain,
skP0(skc2),
inference(res,[status(thm),theory(equality)],[11,21]),
[iquote('0:Res:11.0,21.0')] ).
cnf(375,plain,
( ~ equal(sdtasdt0(u,skc2),xk)
| skP0(u) ),
inference(res,[status(thm),theory(equality)],[5,34]),
[iquote('0:Res:5.0,34.0')] ).
cnf(377,plain,
( ~ equal(sdtasdt0(u,xk),xk)
| skP0(u) ),
inference(res,[status(thm),theory(equality)],[3,34]),
[iquote('0:Res:3.0,34.0')] ).
cnf(378,plain,
( ~ equal(sdtasdt0(u,sz10),xk)
| skP0(u) ),
inference(res,[status(thm),theory(equality)],[2,34]),
[iquote('0:Res:2.0,34.0')] ).
cnf(388,plain,
( ~ skP0(skc2)
| doDivides0(skf7(skc2),skc2)
| equal(skc2,sz00)
| equal(skc2,sz10) ),
inference(res,[status(thm),theory(equality)],[5,45]),
[iquote('0:Res:5.0,45.0')] ).
cnf(389,plain,
( ~ skP0(skc3)
| equal(skc3,sz10)
| equal(skc3,sz00)
| doDivides0(skf7(skc3),skc3) ),
inference(res,[status(thm),theory(equality)],[4,45]),
[iquote('0:Res:4.0,45.0')] ).
cnf(423,plain,
( equal(skc2,sz00)
| doDivides0(skf7(skc2),skc2) ),
inference(mrr,[status(thm)],[388,362,18]),
[iquote('0:MRR:388.0,388.3,362.0,18.0')] ).
cnf(427,plain,
equal(skc2,sz00),
inference(spt,[spt(split,[position(s1)])],[423]),
[iquote('1:Spt:423.0')] ).
cnf(433,plain,
equal(sdtasdt0(sz00,skc3),xk),
inference(rew,[status(thm),theory(equality)],[427,20]),
[iquote('1:Rew:427.0,20.0')] ).
cnf(440,plain,
( ~ aNaturalNumber0(skc3)
| equal(xk,sz00) ),
inference(spr,[status(thm),theory(equality)],[28,433]),
[iquote('1:SpR:28.1,433.0')] ).
cnf(442,plain,
equal(xk,sz00),
inference(ssi,[status(thm)],[440,4]),
[iquote('1:SSi:440.0,4.0')] ).
cnf(443,plain,
$false,
inference(mrr,[status(thm)],[442,16]),
[iquote('1:MRR:442.0,16.0')] ).
cnf(444,plain,
~ equal(skc2,sz00),
inference(spt,[spt(split,[position(sa)])],[443,427]),
[iquote('1:Spt:443.0,423.0,427.0')] ).
cnf(445,plain,
doDivides0(skf7(skc2),skc2),
inference(spt,[spt(split,[position(s2)])],[423]),
[iquote('1:Spt:443.0,423.1')] ).
cnf(464,plain,
( ~ aNaturalNumber0(xk)
| ~ equal(xk,xk)
| skP0(sz10) ),
inference(spl,[status(thm),theory(equality)],[26,377]),
[iquote('0:SpL:26.1,377.0')] ).
cnf(465,plain,
( ~ aNaturalNumber0(xk)
| skP0(sz10) ),
inference(obv,[status(thm),theory(equality)],[464]),
[iquote('0:Obv:464.1')] ).
cnf(466,plain,
skP0(sz10),
inference(ssi,[status(thm)],[465,3]),
[iquote('0:SSi:465.0,3.0')] ).
cnf(537,plain,
( ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(skc2,u),xk)
| skP0(u) ),
inference(spl,[status(thm),theory(equality)],[38,375]),
[iquote('0:SpL:38.2,375.0')] ).
cnf(556,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(skc2,u),xk)
| skP0(u) ),
inference(ssi,[status(thm)],[537,5,362]),
[iquote('0:SSi:537.0,5.0,362.0')] ).
cnf(593,plain,
( ~ aNaturalNumber0(skc3)
| ~ equal(xk,xk)
| skP0(skc3) ),
inference(spl,[status(thm),theory(equality)],[20,556]),
[iquote('0:SpL:20.0,556.1')] ).
cnf(597,plain,
( ~ aNaturalNumber0(skc3)
| skP0(skc3) ),
inference(obv,[status(thm),theory(equality)],[593]),
[iquote('0:Obv:593.1')] ).
cnf(598,plain,
skP0(skc3),
inference(ssi,[status(thm)],[597,4]),
[iquote('0:SSi:597.0,4.0')] ).
cnf(600,plain,
( equal(skc3,sz10)
| equal(skc3,sz00)
| doDivides0(skf7(skc3),skc3) ),
inference(mrr,[status(thm)],[389,598]),
[iquote('0:MRR:389.0,598.0')] ).
cnf(604,plain,
equal(skc3,sz10),
inference(spt,[spt(split,[position(s2s1)])],[600]),
[iquote('2:Spt:600.0')] ).
cnf(606,plain,
equal(sdtasdt0(skc2,sz10),xk),
inference(rew,[status(thm),theory(equality)],[604,20]),
[iquote('2:Rew:604.0,20.0')] ).
cnf(615,plain,
( ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(sz10)
| equal(sdtasdt0(sz10,skc2),xk) ),
inference(spr,[status(thm),theory(equality)],[606,38]),
[iquote('2:SpR:606.0,38.2')] ).
cnf(628,plain,
( ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(sz10)
| equal(skc2,xk) ),
inference(rew,[status(thm),theory(equality)],[26,615]),
[iquote('2:Rew:26.1,615.2')] ).
cnf(629,plain,
equal(skc2,xk),
inference(ssi,[status(thm)],[628,2,466,5,362]),
[iquote('2:SSi:628.1,628.0,2.0,466.0,5.0,362.0')] ).
cnf(630,plain,
$false,
inference(mrr,[status(thm)],[629,19]),
[iquote('2:MRR:629.0,19.0')] ).
cnf(631,plain,
~ equal(skc3,sz10),
inference(spt,[spt(split,[position(s2sa)])],[630,604]),
[iquote('2:Spt:630.0,600.0,604.0')] ).
cnf(632,plain,
( equal(skc3,sz00)
| doDivides0(skf7(skc3),skc3) ),
inference(spt,[spt(split,[position(s2s2)])],[600]),
[iquote('2:Spt:630.0,600.1,600.2')] ).
cnf(634,plain,
equal(skc3,sz00),
inference(spt,[spt(split,[position(s2s2s1)])],[632]),
[iquote('3:Spt:632.0')] ).
cnf(635,plain,
skP0(sz00),
inference(rew,[status(thm),theory(equality)],[634,598]),
[iquote('3:Rew:634.0,598.0')] ).
cnf(638,plain,
equal(sdtasdt0(skc2,sz00),xk),
inference(rew,[status(thm),theory(equality)],[634,20]),
[iquote('3:Rew:634.0,20.0')] ).
cnf(647,plain,
( ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(sz00)
| equal(sdtasdt0(sz00,skc2),xk) ),
inference(spr,[status(thm),theory(equality)],[638,38]),
[iquote('3:SpR:638.0,38.2')] ).
cnf(660,plain,
( ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(sz00)
| equal(xk,sz00) ),
inference(rew,[status(thm),theory(equality)],[28,647]),
[iquote('3:Rew:28.1,647.2')] ).
cnf(661,plain,
equal(xk,sz00),
inference(ssi,[status(thm)],[660,1,635,5,362]),
[iquote('3:SSi:660.1,660.0,1.0,635.0,5.0,362.0')] ).
cnf(662,plain,
$false,
inference(mrr,[status(thm)],[661,16]),
[iquote('3:MRR:661.0,16.0')] ).
cnf(663,plain,
~ equal(skc3,sz00),
inference(spt,[spt(split,[position(s2s2sa)])],[662,634]),
[iquote('3:Spt:662.0,632.0,634.0')] ).
cnf(664,plain,
doDivides0(skf7(skc3),skc3),
inference(spt,[spt(split,[position(s2s2s2)])],[632]),
[iquote('3:Spt:662.0,632.1')] ).
cnf(706,plain,
( ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(skc3)
| equal(skc3,sz00)
| sdtlseqdt0(skc2,xk) ),
inference(spr,[status(thm),theory(equality)],[20,41]),
[iquote('0:SpR:20.0,41.3')] ).
cnf(707,plain,
( equal(skc3,sz00)
| sdtlseqdt0(skc2,xk) ),
inference(ssi,[status(thm)],[706,4,598,5,362]),
[iquote('0:SSi:706.1,706.0,4.0,598.0,5.0,362.0')] ).
cnf(708,plain,
sdtlseqdt0(skc2,xk),
inference(mrr,[status(thm)],[707,663]),
[iquote('3:MRR:707.0,663.0')] ).
cnf(819,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(skf10(v,u))
| ~ doDivides0(v,u)
| ~ equal(u,xk)
| skP0(v) ),
inference(spl,[status(thm),theory(equality)],[55,34]),
[iquote('0:SpL:55.3,34.1')] ).
cnf(825,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(u,xk)
| skP0(v) ),
inference(ssi,[status(thm)],[819,15]),
[iquote('0:SSi:819.2,15.0')] ).
cnf(1439,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(skc3)
| ~ aNaturalNumber0(skc2)
| equal(sdtasdt0(skc2,sdtasdt0(skc3,u)),sdtasdt0(xk,u)) ),
inference(spr,[status(thm),theory(equality)],[20,70]),
[iquote('0:SpR:20.0,70.3')] ).
cnf(1452,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(skc2,sdtasdt0(skc3,u)),sdtasdt0(xk,u)) ),
inference(ssi,[status(thm)],[1439,5,362,4,598]),
[iquote('0:SSi:1439.2,1439.1,5.0,362.0,4.0,598.0')] ).
cnf(1510,plain,
( ~ aNaturalNumber0(skc3)
| ~ aNaturalNumber0(sz10)
| equal(sdtasdt0(skc2,skc3),sdtasdt0(xk,sz10)) ),
inference(spr,[status(thm),theory(equality)],[25,1452]),
[iquote('0:SpR:25.1,1452.1')] ).
cnf(1519,plain,
( ~ aNaturalNumber0(skc3)
| ~ aNaturalNumber0(sz10)
| equal(sdtasdt0(xk,sz10),xk) ),
inference(rew,[status(thm),theory(equality)],[20,1510]),
[iquote('0:Rew:20.0,1510.2')] ).
cnf(1520,plain,
equal(sdtasdt0(xk,sz10),xk),
inference(ssi,[status(thm)],[1519,2,466,4,598]),
[iquote('0:SSi:1519.1,1519.0,2.0,466.0,4.0,598.0')] ).
cnf(1550,plain,
( ~ equal(xk,xk)
| skP0(xk) ),
inference(spl,[status(thm),theory(equality)],[1520,378]),
[iquote('0:SpL:1520.0,378.0')] ).
cnf(1552,plain,
skP0(xk),
inference(obv,[status(thm),theory(equality)],[1550]),
[iquote('0:Obv:1550.0')] ).
cnf(1835,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(u)
| ~ doDivides0(u,skc2)
| doDivides0(u,xk) ),
inference(res,[status(thm),theory(equality)],[11,66]),
[iquote('0:Res:11.0,66.3')] ).
cnf(1859,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(u,skc2)
| doDivides0(u,xk) ),
inference(ssi,[status(thm)],[1835,5,362,3,1552]),
[iquote('0:SSi:1835.1,1835.0,5.0,362.0,3.0,1552.0')] ).
cnf(2217,plain,
( ~ aNaturalNumber0(skc2)
| ~ aNaturalNumber0(skf12(skc2))
| ~ iLess0(skc2,xk)
| equal(skc2,sz10)
| equal(skc2,sz00)
| doDivides0(skf12(skc2),xk) ),
inference(res,[status(thm),theory(equality)],[56,1859]),
[iquote('0:Res:56.4,1859.1')] ).
cnf(2233,plain,
( ~ iLess0(skc2,xk)
| equal(skc2,sz10)
| equal(skc2,sz00)
| doDivides0(skf12(skc2),xk) ),
inference(ssi,[status(thm)],[2217,10,5,362]),
[iquote('0:SSi:2217.1,2217.0,10.0,5.0,362.0,5.0,362.0')] ).
cnf(2234,plain,
( ~ iLess0(skc2,xk)
| doDivides0(skf12(skc2),xk) ),
inference(mrr,[status(thm)],[2233,18,444]),
[iquote('1:MRR:2233.1,2233.2,18.0,444.0')] ).
cnf(2418,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(skf12(skc2))
| ~ iLess0(skc2,xk)
| ~ equal(xk,xk)
| skP0(skf12(skc2)) ),
inference(res,[status(thm),theory(equality)],[2234,825]),
[iquote('1:Res:2234.1,825.2')] ).
cnf(2420,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(skf12(skc2))
| ~ iLess0(skc2,xk)
| skP0(skf12(skc2)) ),
inference(obv,[status(thm),theory(equality)],[2418]),
[iquote('1:Obv:2418.3')] ).
cnf(2421,plain,
( ~ iLess0(skc2,xk)
| skP0(skf12(skc2)) ),
inference(ssi,[status(thm)],[2420,10,5,362,3,1552]),
[iquote('1:SSi:2420.1,2420.0,10.0,5.0,362.0,3.0,1552.0')] ).
cnf(2427,plain,
( ~ aNaturalNumber0(skc2)
| ~ iLess0(skc2,xk)
| ~ iLess0(skc2,xk)
| equal(skc2,sz00)
| equal(skc2,sz10) ),
inference(ems,[status(thm)],[29,2421,10,50]),
[iquote('1:EmS:29.0,29.1,29.2,2421.1,10.0,50.2')] ).
cnf(2429,plain,
( ~ aNaturalNumber0(skc2)
| ~ iLess0(skc2,xk)
| equal(skc2,sz00)
| equal(skc2,sz10) ),
inference(obv,[status(thm),theory(equality)],[2427]),
[iquote('1:Obv:2427.1')] ).
cnf(2430,plain,
( ~ iLess0(skc2,xk)
| equal(skc2,sz00)
| equal(skc2,sz10) ),
inference(ssi,[status(thm)],[2429,5,362]),
[iquote('1:SSi:2429.0,5.0,362.0')] ).
cnf(2431,plain,
~ iLess0(skc2,xk),
inference(mrr,[status(thm)],[2430,444,18]),
[iquote('1:MRR:2430.1,2430.2,444.0,18.0')] ).
cnf(2463,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(skc2)
| ~ sdtlseqdt0(skc2,xk)
| equal(skc2,xk) ),
inference(res,[status(thm),theory(equality)],[46,2431]),
[iquote('1:Res:46.3,2431.0')] ).
cnf(2464,plain,
( ~ sdtlseqdt0(skc2,xk)
| equal(skc2,xk) ),
inference(ssi,[status(thm)],[2463,5,362,3,1552]),
[iquote('1:SSi:2463.1,2463.0,5.0,362.0,3.0,1552.0')] ).
cnf(2465,plain,
$false,
inference(mrr,[status(thm)],[2464,708,19]),
[iquote('3:MRR:2464.0,2464.1,708.0,19.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM483+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %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 : 600
% 0.12/0.33 % DateTime : Wed Jul 6 06:52:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.68/0.85
% 0.68/0.85 SPASS V 3.9
% 0.68/0.85 SPASS beiseite: Proof found.
% 0.68/0.85 % SZS status Theorem
% 0.68/0.85 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.68/0.85 SPASS derived 1291 clauses, backtracked 64 clauses, performed 4 splits and kept 627 clauses.
% 0.68/0.85 SPASS allocated 99665 KBytes.
% 0.68/0.85 SPASS spent 0:00:00.49 on the problem.
% 0.68/0.85 0:00:00.04 for the input.
% 0.68/0.85 0:00:00.04 for the FLOTTER CNF translation.
% 0.68/0.85 0:00:00.02 for inferences.
% 0.68/0.85 0:00:00.00 for the backtracking.
% 0.68/0.85 0:00:00.35 for the reduction.
% 0.68/0.85
% 0.68/0.85
% 0.68/0.85 Here is a proof with depth 5, length 94 :
% 0.68/0.85 % SZS output start Refutation
% See solution above
% 0.68/0.86 Formulae used in the proof : mSortsC mSortsC_01 m__1716 m__1725 m__1700 mDefDiv m__1716_04 m__ m_MulUnit m_MulZero mMulComm mMonMul2 mIH_03 mDivTrans mMulAsso
% 0.68/0.86
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