TSTP Solution File: NUM424+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM424+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 14:26:03 EDT 2022
% Result : Theorem 5.65s 5.89s
% Output : Refutation 7.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 29
% Syntax : Number of clauses : 130 ( 54 unt; 18 nHn; 130 RR)
% Number of literals : 311 ( 0 equ; 174 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aInteger0(skc1),
file('NUM424+3.p',unknown),
[] ).
cnf(2,axiom,
aInteger0(sz00),
file('NUM424+3.p',unknown),
[] ).
cnf(3,axiom,
aInteger0(sz10),
file('NUM424+3.p',unknown),
[] ).
cnf(4,axiom,
aInteger0(xa),
file('NUM424+3.p',unknown),
[] ).
cnf(5,axiom,
aInteger0(xb),
file('NUM424+3.p',unknown),
[] ).
cnf(6,axiom,
aInteger0(xq),
file('NUM424+3.p',unknown),
[] ).
cnf(9,axiom,
~ equal(xq,sz00),
file('NUM424+3.p',unknown),
[] ).
cnf(10,axiom,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('NUM424+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ aInteger0(u)
| aInteger0(smndt0(u)) ),
file('NUM424+3.p',unknown),
[] ).
cnf(14,axiom,
equal(sdtasdt0(xq,skc1),sdtpldt0(xa,smndt0(xb))),
file('NUM424+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,sz00),u) ),
file('NUM424+3.p',unknown),
[] ).
cnf(16,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('NUM424+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(sz10,u),u) ),
file('NUM424+3.p',unknown),
[] ).
cnf(19,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
file('NUM424+3.p',unknown),
[] ).
cnf(21,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(u,smndt0(u)),sz00) ),
file('NUM424+3.p',unknown),
[] ).
cnf(22,axiom,
( ~ aInteger0(u)
| equal(sdtpldt0(smndt0(u),u),sz00) ),
file('NUM424+3.p',unknown),
[] ).
cnf(23,axiom,
( ~ aInteger0(u)
| ~ aDivisorOf0(v,u)
| aInteger0(v) ),
file('NUM424+3.p',unknown),
[] ).
cnf(24,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtpldt0(v,u)) ),
file('NUM424+3.p',unknown),
[] ).
cnf(25,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aInteger0(sdtasdt0(v,u)) ),
file('NUM424+3.p',unknown),
[] ).
cnf(26,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(smndt0(sz10),u),smndt0(u)) ),
file('NUM424+3.p',unknown),
[] ).
cnf(27,axiom,
( ~ aInteger0(u)
| equal(sdtasdt0(u,smndt0(sz10)),smndt0(u)) ),
file('NUM424+3.p',unknown),
[] ).
cnf(29,axiom,
( ~ aInteger0(u)
| ~ equal(sdtasdt0(xq,u),sdtpldt0(xb,smndt0(xa))) ),
file('NUM424+3.p',unknown),
[] ).
cnf(30,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM424+3.p',unknown),
[] ).
cnf(32,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(u,sz00)
| sdteqdtlpzmzozddtrp0(v,v,u) ),
file('NUM424+3.p',unknown),
[] ).
cnf(35,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('NUM424+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM424+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ equal(sdtasdt0(w,v),u)
| aDivisorOf0(w,u)
| equal(w,sz00) ),
file('NUM424+3.p',unknown),
[] ).
cnf(38,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| equal(sdtasdt0(sdtpldt0(w,v),u),sdtpldt0(sdtasdt0(w,u),sdtasdt0(v,u))) ),
file('NUM424+3.p',unknown),
[] ).
cnf(40,axiom,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ aDivisorOf0(u,sdtpldt0(w,smndt0(v)))
| equal(u,sz00)
| sdteqdtlpzmzozddtrp0(w,v,u) ),
file('NUM424+3.p',unknown),
[] ).
cnf(54,plain,
~ equal(sdtasdt0(xq,skc1),sdtpldt0(xb,smndt0(xa))),
inference(res,[status(thm),theory(equality)],[1,29]),
[iquote('0:Res:1.0,29.0')] ).
cnf(58,plain,
equal(sdtasdt0(smndt0(sz10),skc1),smndt0(skc1)),
inference(res,[status(thm),theory(equality)],[1,26]),
[iquote('0:Res:1.0,26.0')] ).
cnf(59,plain,
equal(sdtasdt0(skc1,smndt0(sz10)),smndt0(skc1)),
inference(res,[status(thm),theory(equality)],[1,27]),
[iquote('0:Res:1.0,27.0')] ).
cnf(60,plain,
equal(sdtpldt0(skc1,smndt0(skc1)),sz00),
inference(res,[status(thm),theory(equality)],[1,21]),
[iquote('0:Res:1.0,21.0')] ).
cnf(61,plain,
equal(sdtpldt0(smndt0(skc1),skc1),sz00),
inference(res,[status(thm),theory(equality)],[1,22]),
[iquote('0:Res:1.0,22.0')] ).
cnf(63,plain,
equal(sdtpldt0(skc1,sz00),skc1),
inference(res,[status(thm),theory(equality)],[1,15]),
[iquote('0:Res:1.0,15.0')] ).
cnf(66,plain,
equal(sdtasdt0(sz10,skc1),skc1),
inference(res,[status(thm),theory(equality)],[1,18]),
[iquote('0:Res:1.0,18.0')] ).
cnf(67,plain,
equal(sdtasdt0(skc1,sz00),sz00),
inference(res,[status(thm),theory(equality)],[1,19]),
[iquote('0:Res:1.0,19.0')] ).
cnf(69,plain,
aInteger0(smndt0(skc1)),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(80,plain,
( ~ aInteger0(u)
| equal(skc1,sz00)
| sdteqdtlpzmzozddtrp0(u,u,skc1) ),
inference(res,[status(thm),theory(equality)],[1,32]),
[iquote('0:Res:1.0,32.1')] ).
cnf(90,plain,
~ equal(sdtpldt0(xb,smndt0(xa)),sdtpldt0(xa,smndt0(xb))),
inference(rew,[status(thm),theory(equality)],[14,54]),
[iquote('0:Rew:14.0,54.0')] ).
cnf(91,plain,
equal(skc1,sz00),
inference(spt,[spt(split,[position(s1)])],[80]),
[iquote('1:Spt:80.1')] ).
cnf(122,plain,
equal(sdtasdt0(xq,sz00),sdtpldt0(xa,smndt0(xb))),
inference(rew,[status(thm),theory(equality)],[91,14]),
[iquote('1:Rew:91.0,14.0')] ).
cnf(185,plain,
( ~ aInteger0(xq)
| equal(sdtpldt0(xa,smndt0(xb)),sz00) ),
inference(spr,[status(thm),theory(equality)],[19,122]),
[iquote('1:SpR:19.1,122.0')] ).
cnf(188,plain,
equal(sdtpldt0(xa,smndt0(xb)),sz00),
inference(ssi,[status(thm)],[185,6]),
[iquote('1:SSi:185.0,6.0')] ).
cnf(191,plain,
~ equal(sdtpldt0(xb,smndt0(xa)),sz00),
inference(rew,[status(thm),theory(equality)],[188,90]),
[iquote('1:Rew:188.0,90.0')] ).
cnf(215,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(smndt0(sz00))
| equal(smndt0(sz00),sz00) ),
inference(spr,[status(thm),theory(equality)],[22,15]),
[iquote('0:SpR:22.1,15.1')] ).
cnf(621,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa)
| equal(sdtpldt0(xa,sdtpldt0(smndt0(xb),u)),sdtpldt0(sz00,u)) ),
inference(spr,[status(thm),theory(equality)],[188,36]),
[iquote('1:SpR:188.0,36.3')] ).
cnf(622,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(u))
| ~ aInteger0(u)
| equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(sz00,v)) ),
inference(spr,[status(thm),theory(equality)],[21,36]),
[iquote('0:SpR:21.1,36.3')] ).
cnf(625,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| equal(sdtpldt0(smndt0(u),sdtpldt0(u,v)),sdtpldt0(sz00,v)) ),
inference(spr,[status(thm),theory(equality)],[22,36]),
[iquote('0:SpR:22.1,36.3')] ).
cnf(629,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(xb))
| ~ aInteger0(xa)
| equal(sdtpldt0(xa,sdtpldt0(smndt0(xb),u)),u) ),
inference(rew,[status(thm),theory(equality)],[16,621]),
[iquote('1:Rew:16.1,621.3')] ).
cnf(630,plain,
( ~ aInteger0(u)
| equal(sdtpldt0(xa,sdtpldt0(smndt0(xb),u)),u) ),
inference(ssi,[status(thm)],[629,4,12,5]),
[iquote('1:SSi:629.2,629.1,4.0,12.1,5.0')] ).
cnf(634,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[625]),
[iquote('0:Obv:625.0')] ).
cnf(635,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(smndt0(v))
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(rew,[status(thm),theory(equality)],[16,634]),
[iquote('0:Rew:16.1,634.3')] ).
cnf(636,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),sdtpldt0(v,u)),u) ),
inference(ssi,[status(thm)],[635,12]),
[iquote('0:SSi:635.2,12.1')] ).
cnf(637,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u)) ),
inference(obv,[status(thm),theory(equality)],[622]),
[iquote('0:Obv:622.0')] ).
cnf(638,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(v))
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(rew,[status(thm),theory(equality)],[16,637]),
[iquote('0:Rew:16.1,637.3')] ).
cnf(639,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u) ),
inference(ssi,[status(thm)],[638,12]),
[iquote('0:SSi:638.1,12.1')] ).
cnf(671,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xb)
| equal(sdtpldt0(xa,sz00),xb) ),
inference(spr,[status(thm),theory(equality)],[22,630]),
[iquote('1:SpR:22.1,630.1')] ).
cnf(673,plain,
( ~ aInteger0(xb)
| equal(sdtpldt0(xa,sz00),xb) ),
inference(obv,[status(thm),theory(equality)],[671]),
[iquote('1:Obv:671.0')] ).
cnf(674,plain,
equal(sdtpldt0(xa,sz00),xb),
inference(ssi,[status(thm)],[673,5]),
[iquote('1:SSi:673.0,5.0')] ).
cnf(681,plain,
( ~ aInteger0(xa)
| equal(xb,xa) ),
inference(spr,[status(thm),theory(equality)],[674,15]),
[iquote('1:SpR:674.0,15.1')] ).
cnf(690,plain,
equal(xb,xa),
inference(ssi,[status(thm)],[681,4]),
[iquote('1:SSi:681.0,4.0')] ).
cnf(695,plain,
~ equal(sdtpldt0(xa,smndt0(xa)),sz00),
inference(rew,[status(thm),theory(equality)],[690,191]),
[iquote('1:Rew:690.0,191.0')] ).
cnf(701,plain,
equal(sdtpldt0(xa,smndt0(xa)),sz00),
inference(rew,[status(thm),theory(equality)],[690,188]),
[iquote('1:Rew:690.0,188.0')] ).
cnf(710,plain,
~ equal(sz00,sz00),
inference(rew,[status(thm),theory(equality)],[701,695]),
[iquote('1:Rew:701.0,695.0')] ).
cnf(711,plain,
$false,
inference(obv,[status(thm),theory(equality)],[710]),
[iquote('1:Obv:710.0')] ).
cnf(725,plain,
~ equal(skc1,sz00),
inference(spt,[spt(split,[position(sa)])],[711,91]),
[iquote('1:Spt:711.0,80.1,91.0')] ).
cnf(726,plain,
( ~ aInteger0(u)
| sdteqdtlpzmzozddtrp0(u,u,skc1) ),
inference(spt,[spt(split,[position(s2)])],[80]),
[iquote('1:Spt:711.0,80.0,80.2')] ).
cnf(727,plain,
equal(smndt0(sz00),sz00),
inference(ssi,[status(thm)],[215,12,2]),
[iquote('0:SSi:215.1,215.0,12.0,2.0,2.1')] ).
cnf(794,plain,
( ~ aInteger0(skc1)
| ~ aInteger0(xq)
| aInteger0(sdtpldt0(xa,smndt0(xb))) ),
inference(spr,[status(thm),theory(equality)],[14,25]),
[iquote('0:SpR:14.0,25.2')] ).
cnf(797,plain,
aInteger0(sdtpldt0(xa,smndt0(xb))),
inference(ssi,[status(thm)],[794,6,1]),
[iquote('0:SSi:794.1,794.0,6.0,1.0')] ).
cnf(869,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(skc1)
| equal(sdtasdt0(smndt0(skc1),u),sdtasdt0(skc1,sdtasdt0(smndt0(sz10),u))) ),
inference(spr,[status(thm),theory(equality)],[59,35]),
[iquote('0:SpR:59.0,35.3')] ).
cnf(872,plain,
( ~ aInteger0(u)
| ~ aInteger0(skc1)
| ~ aInteger0(smndt0(sz10))
| equal(sdtasdt0(smndt0(skc1),u),sdtasdt0(smndt0(sz10),sdtasdt0(skc1,u))) ),
inference(spr,[status(thm),theory(equality)],[58,35]),
[iquote('0:SpR:58.0,35.3')] ).
cnf(873,plain,
( ~ aInteger0(u)
| ~ aInteger0(skc1)
| ~ aInteger0(xq)
| equal(sdtasdt0(sdtpldt0(xa,smndt0(xb)),u),sdtasdt0(xq,sdtasdt0(skc1,u))) ),
inference(spr,[status(thm),theory(equality)],[14,35]),
[iquote('0:SpR:14.0,35.3')] ).
cnf(881,plain,
( ~ aInteger0(u)
| equal(sdtasdt0(sdtpldt0(xa,smndt0(xb)),u),sdtasdt0(xq,sdtasdt0(skc1,u))) ),
inference(ssi,[status(thm)],[873,6,1]),
[iquote('0:SSi:873.2,873.1,6.0,1.0')] ).
cnf(882,plain,
( ~ aInteger0(u)
| equal(sdtasdt0(smndt0(skc1),u),sdtasdt0(smndt0(sz10),sdtasdt0(skc1,u))) ),
inference(ssi,[status(thm)],[872,12,3,1]),
[iquote('0:SSi:872.2,872.1,12.0,3.0,1.1')] ).
cnf(883,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(skc1)
| equal(sdtasdt0(smndt0(skc1),u),sdtasdt0(skc1,smndt0(u))) ),
inference(rew,[status(thm),theory(equality)],[26,869]),
[iquote('0:Rew:26.1,869.3')] ).
cnf(884,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(skc1)
| equal(sdtasdt0(smndt0(sz10),sdtasdt0(skc1,u)),sdtasdt0(skc1,smndt0(u))) ),
inference(rew,[status(thm),theory(equality)],[882,883]),
[iquote('0:Rew:882.1,883.3')] ).
cnf(885,plain,
( ~ aInteger0(u)
| equal(sdtasdt0(smndt0(sz10),sdtasdt0(skc1,u)),sdtasdt0(skc1,smndt0(u))) ),
inference(ssi,[status(thm)],[884,1,12,3]),
[iquote('0:SSi:884.2,884.1,1.0,12.1,3.0')] ).
cnf(886,plain,
( ~ aInteger0(u)
| equal(sdtasdt0(smndt0(skc1),u),sdtasdt0(skc1,smndt0(u))) ),
inference(rew,[status(thm),theory(equality)],[885,882]),
[iquote('0:Rew:885.1,882.1')] ).
cnf(948,plain,
( ~ aInteger0(sdtasdt0(u,v))
| ~ aInteger0(v)
| ~ aInteger0(u)
| aDivisorOf0(u,sdtasdt0(u,v))
| equal(u,sz00) ),
inference(eqr,[status(thm),theory(equality)],[37]),
[iquote('0:EqR:37.3')] ).
cnf(968,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| aDivisorOf0(v,sdtasdt0(v,u))
| equal(v,sz00) ),
inference(ssi,[status(thm)],[948,25]),
[iquote('0:SSi:948.0,25.2')] ).
cnf(1109,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(sdtpldt0(v,u))
| equal(sdtpldt0(sdtasdt0(v,smndt0(sz10)),sdtasdt0(u,smndt0(sz10))),smndt0(sdtpldt0(v,u))) ),
inference(spr,[status(thm),theory(equality)],[38,27]),
[iquote('0:SpR:38.3,27.1')] ).
cnf(1172,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(sdtpldt0(v,u))
| equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
inference(rew,[status(thm),theory(equality)],[27,1109]),
[iquote('0:Rew:27.1,1109.4,27.1,1109.4')] ).
cnf(1173,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),smndt0(u)),smndt0(sdtpldt0(v,u))) ),
inference(ssi,[status(thm)],[1172,24,12,3]),
[iquote('0:SSi:1172.3,1172.0,24.0,12.1,3.2')] ).
cnf(1329,plain,
( ~ aInteger0(smndt0(u))
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aDivisorOf0(w,sdtpldt0(smndt0(u),v))
| equal(w,sz00)
| sdteqdtlpzmzozddtrp0(v,u,w) ),
inference(spl,[status(thm),theory(equality)],[30,40]),
[iquote('0:SpL:30.2,40.3')] ).
cnf(1345,plain,
( ~ aInteger0(smndt0(u))
| ~ aInteger0(v)
| ~ aInteger0(u)
| ~ aInteger0(w)
| ~ aDivisorOf0(v,sdtpldt0(smndt0(u),w))
| equal(v,sz00)
| sdteqdtlpzmzozddtrp0(w,u,v) ),
inference(obv,[status(thm),theory(equality)],[1329]),
[iquote('0:Obv:1329.1')] ).
cnf(1346,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ aDivisorOf0(u,sdtpldt0(smndt0(v),w))
| equal(u,sz00)
| sdteqdtlpzmzozddtrp0(w,v,u) ),
inference(ssi,[status(thm)],[1345,12]),
[iquote('0:SSi:1345.0,12.1')] ).
cnf(1470,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(smndt0(skc1))
| equal(sdtasdt0(skc1,smndt0(smndt0(sz10))),smndt0(smndt0(skc1))) ),
inference(spr,[status(thm),theory(equality)],[886,27]),
[iquote('0:SpR:886.1,27.1')] ).
cnf(1486,plain,
equal(sdtasdt0(skc1,smndt0(smndt0(sz10))),smndt0(smndt0(skc1))),
inference(ssi,[status(thm)],[1470,12,1,3]),
[iquote('0:SSi:1470.1,1470.0,12.0,1.1,12.0,3.1')] ).
cnf(1639,plain,
( ~ aInteger0(skc1)
| ~ aInteger0(smndt0(skc1))
| equal(sdtpldt0(smndt0(smndt0(skc1)),sz00),skc1) ),
inference(spr,[status(thm),theory(equality)],[61,636]),
[iquote('0:SpR:61.0,636.2')] ).
cnf(1645,plain,
equal(sdtpldt0(smndt0(smndt0(skc1)),sz00),skc1),
inference(ssi,[status(thm)],[1639,12,1]),
[iquote('0:SSi:1639.1,1639.0,12.0,1.0,1.1')] ).
cnf(1671,plain,
( ~ aInteger0(smndt0(smndt0(skc1)))
| equal(smndt0(smndt0(skc1)),skc1) ),
inference(spr,[status(thm),theory(equality)],[1645,15]),
[iquote('0:SpR:1645.0,15.1')] ).
cnf(1680,plain,
equal(smndt0(smndt0(skc1)),skc1),
inference(ssi,[status(thm)],[1671,12,1]),
[iquote('0:SSi:1671.0,12.0,12.1,1.1')] ).
cnf(1681,plain,
equal(sdtasdt0(skc1,smndt0(smndt0(sz10))),skc1),
inference(rew,[status(thm),theory(equality)],[1680,1486]),
[iquote('0:Rew:1680.0,1486.0')] ).
cnf(1740,plain,
( ~ aInteger0(smndt0(u))
| ~ aInteger0(smndt0(smndt0(u)))
| ~ aInteger0(u)
| equal(sdtpldt0(u,sz00),smndt0(smndt0(u))) ),
inference(spr,[status(thm),theory(equality)],[21,639]),
[iquote('0:SpR:21.1,639.2')] ).
cnf(1754,plain,
( ~ aInteger0(smndt0(u))
| ~ aInteger0(smndt0(smndt0(u)))
| ~ aInteger0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(rew,[status(thm),theory(equality)],[15,1740]),
[iquote('0:Rew:15.1,1740.3')] ).
cnf(1755,plain,
( ~ aInteger0(u)
| equal(smndt0(smndt0(u)),u) ),
inference(ssi,[status(thm)],[1754,12]),
[iquote('0:SSi:1754.1,1754.0,12.1,12.1,12.1')] ).
cnf(1899,plain,
( ~ aInteger0(skc1)
| ~ aInteger0(sz10)
| aDivisorOf0(sz10,skc1)
| equal(sz10,sz00) ),
inference(spr,[status(thm),theory(equality)],[66,968]),
[iquote('0:SpR:66.0,968.2')] ).
cnf(1901,plain,
( ~ aInteger0(skc1)
| ~ aInteger0(smndt0(sz10))
| aDivisorOf0(smndt0(sz10),smndt0(skc1))
| equal(smndt0(sz10),sz00) ),
inference(spr,[status(thm),theory(equality)],[58,968]),
[iquote('0:SpR:58.0,968.2')] ).
cnf(1912,plain,
( aDivisorOf0(sz10,skc1)
| equal(sz10,sz00) ),
inference(ssi,[status(thm)],[1899,3,1]),
[iquote('0:SSi:1899.1,1899.0,3.0,1.0')] ).
cnf(1919,plain,
( aDivisorOf0(smndt0(sz10),smndt0(skc1))
| equal(smndt0(sz10),sz00) ),
inference(ssi,[status(thm)],[1901,12,3,1]),
[iquote('0:SSi:1901.1,1901.0,12.0,3.0,1.1')] ).
cnf(1943,plain,
equal(sz10,sz00),
inference(spt,[spt(split,[position(s2s1)])],[1912]),
[iquote('2:Spt:1912.1')] ).
cnf(1950,plain,
equal(sdtasdt0(skc1,smndt0(smndt0(sz00))),skc1),
inference(rew,[status(thm),theory(equality)],[1943,1681]),
[iquote('2:Rew:1943.0,1681.0')] ).
cnf(2003,plain,
equal(skc1,sz00),
inference(rew,[status(thm),theory(equality)],[67,1950,727]),
[iquote('2:Rew:67.0,1950.0,727.0,1950.0,727.0,1950.0')] ).
cnf(2004,plain,
$false,
inference(mrr,[status(thm)],[2003,725]),
[iquote('2:MRR:2003.0,725.0')] ).
cnf(2335,plain,
~ equal(sz10,sz00),
inference(spt,[spt(split,[position(s2sa)])],[2004,1943]),
[iquote('2:Spt:2004.0,1912.1,1943.0')] ).
cnf(2336,plain,
aDivisorOf0(sz10,skc1),
inference(spt,[spt(split,[position(s2s2)])],[1912]),
[iquote('2:Spt:2004.0,1912.0')] ).
cnf(2454,plain,
equal(smndt0(sz10),sz00),
inference(spt,[spt(split,[position(s2s2s1)])],[1919]),
[iquote('3:Spt:1919.1')] ).
cnf(2456,plain,
equal(sdtasdt0(skc1,sz00),smndt0(skc1)),
inference(rew,[status(thm),theory(equality)],[2454,59]),
[iquote('3:Rew:2454.0,59.0')] ).
cnf(2467,plain,
equal(smndt0(skc1),sz00),
inference(rew,[status(thm),theory(equality)],[67,2456]),
[iquote('3:Rew:67.0,2456.0')] ).
cnf(2474,plain,
equal(sdtpldt0(skc1,sz00),sz00),
inference(rew,[status(thm),theory(equality)],[2467,60]),
[iquote('3:Rew:2467.0,60.0')] ).
cnf(2493,plain,
equal(skc1,sz00),
inference(rew,[status(thm),theory(equality)],[63,2474]),
[iquote('3:Rew:63.0,2474.0')] ).
cnf(2494,plain,
$false,
inference(mrr,[status(thm)],[2493,725]),
[iquote('3:MRR:2493.0,725.0')] ).
cnf(2824,plain,
~ equal(smndt0(sz10),sz00),
inference(spt,[spt(split,[position(s2s2sa)])],[2494,2454]),
[iquote('3:Spt:2494.0,1919.1,2454.0')] ).
cnf(2825,plain,
aDivisorOf0(smndt0(sz10),smndt0(skc1)),
inference(spt,[spt(split,[position(s2s2s2)])],[1919]),
[iquote('3:Spt:2494.0,1919.0')] ).
cnf(2835,plain,
( ~ aInteger0(smndt0(skc1))
| aInteger0(smndt0(sz10)) ),
inference(res,[status(thm),theory(equality)],[2825,23]),
[iquote('3:Res:2825.0,23.1')] ).
cnf(2836,plain,
aInteger0(smndt0(sz10)),
inference(mrr,[status(thm)],[2835,69]),
[iquote('3:MRR:2835.0,69.0')] ).
cnf(7141,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| equal(sdtasdt0(xq,sdtasdt0(skc1,smndt0(sz10))),smndt0(sdtpldt0(xa,smndt0(xb)))) ),
inference(spr,[status(thm),theory(equality)],[881,27]),
[iquote('0:SpR:881.1,27.1')] ).
cnf(7175,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| equal(sdtasdt0(xq,smndt0(skc1)),smndt0(sdtpldt0(xa,smndt0(xb)))) ),
inference(rew,[status(thm),theory(equality)],[59,7141]),
[iquote('0:Rew:59.0,7141.2')] ).
cnf(7176,plain,
equal(sdtasdt0(xq,smndt0(skc1)),smndt0(sdtpldt0(xa,smndt0(xb)))),
inference(ssi,[status(thm)],[7175,797,2836]),
[iquote('3:SSi:7175.1,7175.0,797.0,2836.0')] ).
cnf(7680,plain,
( ~ aInteger0(smndt0(skc1))
| ~ aInteger0(xq)
| aDivisorOf0(xq,smndt0(sdtpldt0(xa,smndt0(xb))))
| equal(xq,sz00) ),
inference(spr,[status(thm),theory(equality)],[7176,968]),
[iquote('3:SpR:7176.0,968.2')] ).
cnf(7692,plain,
( aDivisorOf0(xq,smndt0(sdtpldt0(xa,smndt0(xb))))
| equal(xq,sz00) ),
inference(ssi,[status(thm)],[7680,6,69]),
[iquote('3:SSi:7680.1,7680.0,6.0,69.0')] ).
cnf(7693,plain,
aDivisorOf0(xq,smndt0(sdtpldt0(xa,smndt0(xb)))),
inference(mrr,[status(thm)],[7692,9]),
[iquote('3:MRR:7692.1,9.0')] ).
cnf(9439,plain,
( ~ aInteger0(u)
| ~ aInteger0(smndt0(u))
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(spr,[status(thm),theory(equality)],[1755,1173]),
[iquote('0:SpR:1755.1,1173.2')] ).
cnf(9472,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| equal(sdtpldt0(smndt0(v),u),smndt0(sdtpldt0(v,smndt0(u)))) ),
inference(ssi,[status(thm)],[9439,12]),
[iquote('0:SSi:9439.1,12.1')] ).
cnf(9474,plain,
( ~ aInteger0(u)
| ~ aInteger0(v)
| ~ aInteger0(w)
| ~ aDivisorOf0(u,smndt0(sdtpldt0(v,smndt0(w))))
| equal(u,sz00)
| sdteqdtlpzmzozddtrp0(w,v,u) ),
inference(rew,[status(thm),theory(equality)],[9472,1346]),
[iquote('0:Rew:9472.2,1346.3')] ).
cnf(18245,plain,
( ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb)
| equal(xq,sz00)
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(res,[status(thm),theory(equality)],[7693,9474]),
[iquote('3:Res:7693.0,9474.3')] ).
cnf(18251,plain,
( equal(xq,sz00)
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(ssi,[status(thm)],[18245,5,4,6]),
[iquote('3:SSi:18245.2,18245.1,18245.0,5.0,4.0,6.0')] ).
cnf(18252,plain,
$false,
inference(mrr,[status(thm)],[18251,9,10]),
[iquote('3:MRR:18251.0,18251.1,9.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM424+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 14:09:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 5.65/5.89
% 5.65/5.89 SPASS V 3.9
% 5.65/5.89 SPASS beiseite: Proof found.
% 5.65/5.89 % SZS status Theorem
% 5.65/5.89 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.65/5.89 SPASS derived 10632 clauses, backtracked 656 clauses, performed 5 splits and kept 2662 clauses.
% 5.65/5.89 SPASS allocated 114139 KBytes.
% 5.65/5.89 SPASS spent 0:00:05.53 on the problem.
% 5.65/5.89 0:00:00.04 for the input.
% 5.65/5.89 0:00:00.03 for the FLOTTER CNF translation.
% 5.65/5.89 0:00:00.10 for inferences.
% 5.65/5.89 0:00:00.10 for the backtracking.
% 5.65/5.89 0:00:05.21 for the reduction.
% 5.65/5.89
% 5.65/5.89
% 5.65/5.89 Here is a proof with depth 4, length 130 :
% 5.65/5.89 % SZS output start Refutation
% See solution above
% 7.86/8.06 Formulae used in the proof : m__ mIntZero mIntOne m__704 mIntNeg mAddZero mMulOne mMulZero mAddNeg mDivisor mIntPlus mIntMult mMulMinOne mAddComm mEquModRef mMulAsso mAddAsso mDistrib mEquMod
% 7.86/8.06
%------------------------------------------------------------------------------