TSTP Solution File: NUM528+3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM528+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 14:27:09 EDT 2022
% Result : Theorem 5.75s 5.90s
% Output : Refutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 36
% Syntax : Number of clauses : 154 ( 49 unt; 47 nHn; 154 RR)
% Number of literals : 464 ( 0 equ; 275 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aNaturalNumber0(sz10),
file('NUM528+3.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM528+3.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM528+3.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM528+3.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM528+3.p',unknown),
[] ).
cnf(8,axiom,
aNaturalNumber0(skc3),
file('NUM528+3.p',unknown),
[] ).
cnf(9,axiom,
aNaturalNumber0(xq),
file('NUM528+3.p',unknown),
[] ).
cnf(15,axiom,
doDivides0(xp,xn),
file('NUM528+3.p',unknown),
[] ).
cnf(16,axiom,
~ equal(sz10,sz00),
file('NUM528+3.p',unknown),
[] ).
cnf(17,axiom,
aNaturalNumber0(skf6(u,v)),
file('NUM528+3.p',unknown),
[] ).
cnf(19,axiom,
~ equal(xn,sz00),
file('NUM528+3.p',unknown),
[] ).
cnf(20,axiom,
~ equal(xm,sz00),
file('NUM528+3.p',unknown),
[] ).
cnf(21,axiom,
~ equal(xp,sz00),
file('NUM528+3.p',unknown),
[] ).
cnf(22,axiom,
~ equal(xp,sz10),
file('NUM528+3.p',unknown),
[] ).
cnf(23,axiom,
doDivides0(xp,sdtasdt0(xn,xn)),
file('NUM528+3.p',unknown),
[] ).
cnf(25,axiom,
equal(sdtasdt0(xp,xq),xn),
file('NUM528+3.p',unknown),
[] ).
cnf(26,axiom,
equal(sdtsldt0(xn,xp),xq),
file('NUM528+3.p',unknown),
[] ).
cnf(30,axiom,
equal(sdtasdt0(xp,skc3),sdtasdt0(xn,xn)),
file('NUM528+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,sz10),u) ),
file('NUM528+3.p',unknown),
[] ).
cnf(37,axiom,
equal(sdtasdt0(xp,sdtasdt0(xm,xm)),sdtasdt0(xn,xn)),
file('NUM528+3.p',unknown),
[] ).
cnf(38,axiom,
equal(sdtasdt0(xp,sdtasdt0(xq,xq)),sdtasdt0(xm,xm)),
file('NUM528+3.p',unknown),
[] ).
cnf(39,axiom,
( ~ skC0
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
file('NUM528+3.p',unknown),
[] ).
cnf(41,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM528+3.p',unknown),
[] ).
cnf(44,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xn,u),xm)
| skC0 ),
file('NUM528+3.p',unknown),
[] ).
cnf(46,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xm,u),xn)
| equal(xn,xm) ),
file('NUM528+3.p',unknown),
[] ).
cnf(47,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(v,u)
| sdtlseqdt0(u,v) ),
file('NUM528+3.p',unknown),
[] ).
cnf(51,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM528+3.p',unknown),
[] ).
cnf(56,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(v,sz00)
| sdtlseqdt0(u,sdtasdt0(u,v)) ),
file('NUM528+3.p',unknown),
[] ).
cnf(64,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| equal(sdtpldt0(v,skf6(u,v)),u) ),
file('NUM528+3.p',unknown),
[] ).
cnf(65,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ sdtlseqdt0(u,v)
| equal(v,u) ),
file('NUM528+3.p',unknown),
[] ).
cnf(70,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM528+3.p',unknown),
[] ).
cnf(77,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtasdt0(sdtasdt0(w,v),u),sdtasdt0(w,sdtasdt0(v,u))) ),
file('NUM528+3.p',unknown),
[] ).
cnf(79,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM528+3.p',unknown),
[] ).
cnf(90,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM528+3.p',unknown),
[] ).
cnf(96,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(w,u)
| equal(w,sz00)
| equal(sdtasdt0(v,sdtsldt0(u,w)),sdtsldt0(sdtasdt0(v,u),w)) ),
file('NUM528+3.p',unknown),
[] ).
cnf(97,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(v,w)
| ~ equal(w,sdtasdt0(v,u))
| equal(u,sdtsldt0(w,v))
| equal(v,sz00) ),
file('NUM528+3.p',unknown),
[] ).
cnf(106,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| equal(v,sz00)
| equal(w,sdtsldt0(u,v)) ),
inference(mrr,[status(thm)],[97,70]),
[iquote('0:MRR:97.3,70.4')] ).
cnf(123,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtpldt0(xm,u),xn) ),
inference(spt,[spt(split,[position(s1)])],[46]),
[iquote('1:Spt:46.0,46.1')] ).
cnf(378,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(v,sz00)
| sdtlseqdt0(u,sdtasdt0(v,u)) ),
inference(spr,[status(thm),theory(equality)],[51,56]),
[iquote('0:SpR:51.2,56.3')] ).
cnf(388,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(v,sz00)
| sdtlseqdt0(u,sdtasdt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[378]),
[iquote('0:Obv:378.1')] ).
cnf(674,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(skf6(u,xn))
| ~ sdtlseqdt0(xn,u)
| ~ equal(u,xm)
| skC0 ),
inference(spl,[status(thm),theory(equality)],[64,44]),
[iquote('0:SpL:64.3,44.1')] ).
cnf(677,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(skf6(u,xm))
| ~ sdtlseqdt0(xm,u)
| ~ equal(u,xn) ),
inference(spl,[status(thm),theory(equality)],[64,123]),
[iquote('1:SpL:64.3,123.1')] ).
cnf(678,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(xm,u)
| ~ equal(u,xn) ),
inference(ssi,[status(thm)],[677,17,4]),
[iquote('1:SSi:677.2,677.1,17.0,4.0,4.0')] ).
cnf(679,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(xn,u)
| ~ equal(u,xm)
| skC0 ),
inference(ssi,[status(thm)],[674,17,3]),
[iquote('0:SSi:674.2,674.1,17.0,3.0,3.0')] ).
cnf(687,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(u)
| ~ equal(u,xn)
| sdtlseqdt0(u,xm) ),
inference(res,[status(thm),theory(equality)],[47,678]),
[iquote('1:Res:47.2,678.1')] ).
cnf(693,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(u)
| ~ equal(u,xn)
| sdtlseqdt0(u,xm) ),
inference(obv,[status(thm),theory(equality)],[687]),
[iquote('1:Obv:687.0')] ).
cnf(694,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xn)
| sdtlseqdt0(u,xm) ),
inference(ssi,[status(thm)],[693,4]),
[iquote('1:SSi:693.0,4.0')] ).
cnf(891,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ skC0
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| equal(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(res,[status(thm),theory(equality)],[39,65]),
[iquote('0:Res:39.1,65.2')] ).
cnf(896,plain,
( ~ skC0
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| equal(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(ssi,[status(thm)],[891,41,3,4]),
[iquote('0:SSi:891.1,891.0,41.0,3.0,3.2,41.0,4.0,4.2')] ).
cnf(899,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| equal(xp,sz00)
| sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(spr,[status(thm),theory(equality)],[37,388]),
[iquote('0:SpR:37.0,388.3')] ).
cnf(907,plain,
( equal(xp,sz00)
| sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(ssi,[status(thm)],[899,6,5,41,4]),
[iquote('0:SSi:899.1,899.0,6.0,5.0,41.2,4.0,4.0')] ).
cnf(908,plain,
sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)),
inference(mrr,[status(thm)],[907,21]),
[iquote('0:MRR:907.0,21.0')] ).
cnf(909,plain,
( ~ skC0
| equal(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(mrr,[status(thm)],[896,908]),
[iquote('0:MRR:896.1,908.0')] ).
cnf(1283,plain,
( ~ aNaturalNumber0(sdtasdt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[70]),
[iquote('0:EqR:70.3')] ).
cnf(1297,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(ssi,[status(thm)],[1283,41]),
[iquote('0:SSi:1283.0,41.2')] ).
cnf(1365,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xq,xq))
| doDivides0(xp,sdtasdt0(xm,xm)) ),
inference(spr,[status(thm),theory(equality)],[38,1297]),
[iquote('0:SpR:38.0,1297.2')] ).
cnf(1387,plain,
doDivides0(xp,sdtasdt0(xm,xm)),
inference(ssi,[status(thm)],[1365,41,9,6,5]),
[iquote('0:SSi:1365.1,1365.0,41.0,9.0,9.0,6.0,5.2')] ).
cnf(1519,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| equal(sdtasdt0(xp,sdtasdt0(xq,u)),sdtasdt0(xn,u)) ),
inference(spr,[status(thm),theory(equality)],[25,77]),
[iquote('0:SpR:25.0,77.3')] ).
cnf(1534,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(xp,sdtasdt0(xq,u)),sdtasdt0(xn,u)) ),
inference(ssi,[status(thm)],[1519,6,5,9]),
[iquote('0:SSi:1519.2,1519.1,6.0,5.0,9.0')] ).
cnf(1791,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ equal(xn,xn)
| ~ equal(xm,xm)
| skC0 ),
inference(res,[status(thm),theory(equality)],[694,679]),
[iquote('1:Res:694.2,679.1')] ).
cnf(1796,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| skC0 ),
inference(obv,[status(thm),theory(equality)],[1791]),
[iquote('1:Obv:1791.3')] ).
cnf(1797,plain,
skC0,
inference(ssi,[status(thm)],[1796,4,3]),
[iquote('1:SSi:1796.1,1796.0,4.0,3.0')] ).
cnf(1801,plain,
equal(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
inference(mrr,[status(thm)],[909,1797]),
[iquote('1:MRR:909.0,1797.0')] ).
cnf(3493,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xn)
| ~ equal(u,xq)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[26,79]),
[iquote('0:SpL:26.0,79.3')] ).
cnf(3494,plain,
( ~ doDivides0(xp,xn)
| ~ equal(u,xq)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[3493,5,6,3]),
[iquote('0:SSi:3493.1,3493.0,5.0,6.0,3.0')] ).
cnf(3495,plain,
( ~ equal(u,xq)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[3494,15,21]),
[iquote('0:MRR:3494.0,3494.3,15.0,21.0')] ).
cnf(3829,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz10)
| ~ equal(v,u)
| equal(u,sz00)
| equal(sdtsldt0(v,u),sz10) ),
inference(spl,[status(thm),theory(equality)],[33,106]),
[iquote('0:SpL:33.1,106.3')] ).
cnf(3839,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xn,sz00)
| equal(sdtsldt0(u,xn),xn) ),
inference(spl,[status(thm),theory(equality)],[1801,106]),
[iquote('1:SpL:1801.0,106.3')] ).
cnf(3848,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xn,sz00)
| equal(sdtsldt0(u,xn),xn) ),
inference(obv,[status(thm),theory(equality)],[3839]),
[iquote('1:Obv:3839.1')] ).
cnf(3849,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xn,sz00)
| equal(sdtsldt0(u,xn),xn) ),
inference(ssi,[status(thm)],[3848,3]),
[iquote('1:SSi:3848.1,3.0')] ).
cnf(3850,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(sdtsldt0(u,xn),xn) ),
inference(mrr,[status(thm)],[3849,19]),
[iquote('1:MRR:3849.2,19.0')] ).
cnf(3853,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sz10)
| ~ equal(u,v)
| equal(v,sz00)
| equal(sdtsldt0(u,v),sz10) ),
inference(obv,[status(thm),theory(equality)],[3829]),
[iquote('0:Obv:3829.0')] ).
cnf(3854,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(u,v)
| equal(v,sz00)
| equal(sdtsldt0(u,v),sz10) ),
inference(ssi,[status(thm)],[3853,2]),
[iquote('0:SSi:3853.2,2.0')] ).
cnf(4322,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xn)
| ~ equal(u,xq)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),xn) ),
inference(spl,[status(thm),theory(equality)],[26,90]),
[iquote('0:SpL:26.0,90.3')] ).
cnf(4323,plain,
( ~ doDivides0(xp,xn)
| ~ equal(u,xq)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),xn) ),
inference(ssi,[status(thm)],[4322,5,6,3]),
[iquote('0:SSi:4322.1,4322.0,5.0,6.0,3.0')] ).
cnf(4324,plain,
( ~ equal(u,xq)
| equal(sdtasdt0(xp,u),xn) ),
inference(mrr,[status(thm)],[4323,15,21]),
[iquote('0:MRR:4323.0,4323.2,15.0,21.0')] ).
cnf(4327,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xq)
| equal(sdtasdt0(u,xp),xn) ),
inference(spr,[status(thm),theory(equality)],[4324,51]),
[iquote('0:SpR:4324.1,51.2')] ).
cnf(4354,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xq)
| equal(sdtasdt0(u,xp),xn) ),
inference(ssi,[status(thm)],[4327,5,6]),
[iquote('0:SSi:4327.1,5.0,6.0')] ).
cnf(4355,plain,
( ~ equal(u,xq)
| equal(sdtasdt0(u,xp),xn) ),
inference(mrr,[status(thm)],[4354,3495]),
[iquote('0:MRR:4354.0,3495.1')] ).
cnf(4718,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xn)
| equal(xp,sz00)
| equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
inference(spr,[status(thm),theory(equality)],[26,96]),
[iquote('0:SpR:26.0,96.5')] ).
cnf(4728,plain,
( ~ aNaturalNumber0(u)
| ~ doDivides0(xp,xn)
| equal(xp,sz00)
| equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
inference(ssi,[status(thm)],[4718,5,6,3]),
[iquote('0:SSi:4718.2,4718.0,5.0,6.0,3.0')] ).
cnf(4729,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xn),xp)) ),
inference(mrr,[status(thm)],[4728,15,21]),
[iquote('0:MRR:4728.1,4728.2,15.0,21.0')] ).
cnf(6534,plain,
( ~ aNaturalNumber0(xq)
| equal(sdtasdt0(xn,xq),sdtasdt0(xm,xm)) ),
inference(spr,[status(thm),theory(equality)],[1534,38]),
[iquote('0:SpR:1534.1,38.0')] ).
cnf(6540,plain,
( ~ aNaturalNumber0(xp)
| ~ equal(xq,xq)
| equal(sdtasdt0(xp,xn),sdtasdt0(xn,xp)) ),
inference(spr,[status(thm),theory(equality)],[4355,1534]),
[iquote('0:SpR:4355.1,1534.1')] ).
cnf(6564,plain,
( ~ aNaturalNumber0(xp)
| equal(sdtasdt0(xp,xn),sdtasdt0(xn,xp)) ),
inference(obv,[status(thm),theory(equality)],[6540]),
[iquote('0:Obv:6540.1')] ).
cnf(6565,plain,
equal(sdtasdt0(xp,xn),sdtasdt0(xn,xp)),
inference(ssi,[status(thm)],[6564,5,6]),
[iquote('0:SSi:6564.0,5.0,6.0')] ).
cnf(7834,plain,
equal(sdtasdt0(xn,xq),sdtasdt0(xm,xm)),
inference(mrr,[status(thm)],[6534,9]),
[iquote('0:MRR:6534.0,9.0')] ).
cnf(8672,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xq)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xn,sz00)
| equal(sdtsldt0(u,xn),xq) ),
inference(spl,[status(thm),theory(equality)],[7834,106]),
[iquote('0:SpL:7834.0,106.3')] ).
cnf(8688,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xq)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xn,sz00)
| equal(xq,xn) ),
inference(rew,[status(thm),theory(equality)],[3850,8672]),
[iquote('1:Rew:3850.2,8672.5')] ).
cnf(8689,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xn,sz00)
| equal(xq,xn) ),
inference(ssi,[status(thm)],[8688,9,3]),
[iquote('1:SSi:8688.2,8688.1,9.0,3.0')] ).
cnf(8690,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xq,xn) ),
inference(mrr,[status(thm)],[8689,19]),
[iquote('1:MRR:8689.2,19.0')] ).
cnf(9319,plain,
( ~ aNaturalNumber0(xn)
| equal(sdtsldt0(sdtasdt0(xn,xn),xp),sdtasdt0(xm,xm)) ),
inference(spr,[status(thm),theory(equality)],[4729,7834]),
[iquote('0:SpR:4729.1,7834.0')] ).
cnf(9344,plain,
( ~ aNaturalNumber0(xn)
| equal(sdtsldt0(sdtasdt0(xm,xm),xp),sdtasdt0(xm,xm)) ),
inference(rew,[status(thm),theory(equality)],[1801,9319]),
[iquote('1:Rew:1801.0,9319.1')] ).
cnf(9345,plain,
equal(sdtsldt0(sdtasdt0(xm,xm),xp),sdtasdt0(xm,xm)),
inference(ssi,[status(thm)],[9344,3]),
[iquote('1:SSi:9344.0,3.0')] ).
cnf(9413,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xm,xm))
| ~ equal(u,sdtasdt0(xm,xm))
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[9345,79]),
[iquote('1:SpL:9345.0,79.3')] ).
cnf(9416,plain,
( ~ doDivides0(xp,sdtasdt0(xm,xm))
| ~ equal(u,sdtasdt0(xm,xm))
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[9413,6,5,41,4]),
[iquote('1:SSi:9413.1,9413.0,6.0,5.0,41.2,4.0,4.0')] ).
cnf(9417,plain,
( ~ equal(u,sdtasdt0(xm,xm))
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[9416,1387,21]),
[iquote('1:MRR:9416.0,9416.3,1387.0,21.0')] ).
cnf(9425,plain,
( ~ equal(u,sdtasdt0(xm,xm))
| equal(xq,xn) ),
inference(mrr,[status(thm)],[8690,9417]),
[iquote('1:MRR:8690.0,9417.1')] ).
cnf(9426,plain,
equal(xq,xn),
inference(aed,[status(thm),theory(equality)],[16,9425]),
[iquote('1:AED:16.0,9425.0')] ).
cnf(9434,plain,
equal(sdtasdt0(xp,xn),xn),
inference(rew,[status(thm),theory(equality)],[9426,25]),
[iquote('1:Rew:9426.0,25.0')] ).
cnf(9447,plain,
( ~ equal(u,xn)
| aNaturalNumber0(u) ),
inference(rew,[status(thm),theory(equality)],[9426,3495]),
[iquote('1:Rew:9426.0,3495.0')] ).
cnf(9588,plain,
equal(sdtasdt0(xn,xp),xn),
inference(rew,[status(thm),theory(equality)],[6565,9434]),
[iquote('1:Rew:6565.0,9434.0')] ).
cnf(9842,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xn)
| equal(xn,sz00)
| equal(sdtsldt0(u,xn),xp) ),
inference(spl,[status(thm),theory(equality)],[9588,106]),
[iquote('1:SpL:9588.0,106.3')] ).
cnf(9852,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xn)
| equal(xn,sz00)
| equal(xp,sz10) ),
inference(rew,[status(thm),theory(equality)],[3854,9842]),
[iquote('1:Rew:3854.4,9842.5')] ).
cnf(9853,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xn)
| equal(xn,sz00)
| equal(xp,sz10) ),
inference(ssi,[status(thm)],[9852,6,5,3]),
[iquote('1:SSi:9852.2,9852.1,6.0,5.0,3.0')] ).
cnf(9854,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xn) ),
inference(mrr,[status(thm)],[9853,19,22]),
[iquote('1:MRR:9853.2,9853.3,19.0,22.0')] ).
cnf(9855,plain,
~ equal(u,xn),
inference(mrr,[status(thm)],[9854,9447]),
[iquote('1:MRR:9854.0,9447.1')] ).
cnf(9856,plain,
$false,
inference(unc,[status(thm)],[9855,9588]),
[iquote('1:UnC:9855.0,9588.0')] ).
cnf(9863,plain,
equal(xn,xm),
inference(spt,[spt(split,[position(s2)])],[46]),
[iquote('1:Spt:9856.0,46.2')] ).
cnf(9963,plain,
doDivides0(xp,sdtasdt0(xm,xm)),
inference(rew,[status(thm),theory(equality)],[9863,23]),
[iquote('1:Rew:9863.0,23.0')] ).
cnf(9964,plain,
equal(sdtasdt0(xp,xq),xm),
inference(rew,[status(thm),theory(equality)],[9863,25]),
[iquote('1:Rew:9863.0,25.0')] ).
cnf(9965,plain,
equal(sdtsldt0(xm,xp),xq),
inference(rew,[status(thm),theory(equality)],[9863,26]),
[iquote('1:Rew:9863.0,26.0')] ).
cnf(9979,plain,
equal(sdtasdt0(xp,skc3),sdtasdt0(xm,xm)),
inference(rew,[status(thm),theory(equality)],[9863,30]),
[iquote('1:Rew:9863.0,30.0')] ).
cnf(9982,plain,
equal(sdtasdt0(xm,xq),sdtasdt0(xm,xm)),
inference(rew,[status(thm),theory(equality)],[9863,7834]),
[iquote('1:Rew:9863.0,7834.0')] ).
cnf(9986,plain,
equal(sdtasdt0(xp,xm),sdtasdt0(xm,xp)),
inference(rew,[status(thm),theory(equality)],[9863,6565]),
[iquote('1:Rew:9863.0,6565.0')] ).
cnf(10000,plain,
equal(sdtasdt0(xp,sdtasdt0(xm,xm)),sdtasdt0(xm,xm)),
inference(rew,[status(thm),theory(equality)],[9863,37]),
[iquote('1:Rew:9863.0,37.0')] ).
cnf(10057,plain,
( ~ aNaturalNumber0(u)
| equal(sdtasdt0(u,xq),sdtsldt0(sdtasdt0(u,xm),xp)) ),
inference(rew,[status(thm),theory(equality)],[9863,4729]),
[iquote('1:Rew:9863.0,4729.1')] ).
cnf(10449,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(skc3)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xp,sz00)
| equal(sdtsldt0(u,xp),skc3) ),
inference(spl,[status(thm),theory(equality)],[9979,106]),
[iquote('1:SpL:9979.0,106.3')] ).
cnf(10460,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xp,sz00)
| equal(sdtsldt0(u,xp),skc3) ),
inference(ssi,[status(thm)],[10449,8,6,5]),
[iquote('1:SSi:10449.2,10449.1,8.0,6.0,5.0')] ).
cnf(10461,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(sdtsldt0(u,xp),skc3) ),
inference(mrr,[status(thm)],[10460,21]),
[iquote('1:MRR:10460.2,21.0')] ).
cnf(10575,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xp,sz00)
| equal(sdtasdt0(xm,xm),sdtsldt0(u,xp)) ),
inference(spl,[status(thm),theory(equality)],[10000,106]),
[iquote('1:SpL:10000.0,106.3')] ).
cnf(10586,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xp,sz00)
| equal(sdtasdt0(xm,xm),skc3) ),
inference(rew,[status(thm),theory(equality)],[10461,10575]),
[iquote('1:Rew:10461.2,10575.5')] ).
cnf(10587,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(xp,sz00)
| equal(sdtasdt0(xm,xm),skc3) ),
inference(ssi,[status(thm)],[10586,41,4,6,5]),
[iquote('1:SSi:10586.2,10586.1,41.0,4.0,4.0,6.0,5.2')] ).
cnf(10588,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,sdtasdt0(xm,xm))
| equal(sdtasdt0(xm,xm),skc3) ),
inference(mrr,[status(thm)],[10587,21]),
[iquote('1:MRR:10587.2,21.0')] ).
cnf(13230,plain,
( ~ aNaturalNumber0(xm)
| equal(sdtsldt0(sdtasdt0(xm,xm),xp),sdtasdt0(xm,xm)) ),
inference(spr,[status(thm),theory(equality)],[10057,9982]),
[iquote('1:SpR:10057.1,9982.0')] ).
cnf(13258,plain,
equal(sdtsldt0(sdtasdt0(xm,xm),xp),sdtasdt0(xm,xm)),
inference(ssi,[status(thm)],[13230,4]),
[iquote('1:SSi:13230.0,4.0')] ).
cnf(13342,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xm,xm))
| ~ equal(u,sdtasdt0(xm,xm))
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[13258,79]),
[iquote('1:SpL:13258.0,79.3')] ).
cnf(13347,plain,
( ~ doDivides0(xp,sdtasdt0(xm,xm))
| ~ equal(u,sdtasdt0(xm,xm))
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[13342,5,6,41,4]),
[iquote('1:SSi:13342.1,13342.0,5.0,6.0,41.2,4.0,4.0')] ).
cnf(13348,plain,
( ~ equal(u,sdtasdt0(xm,xm))
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[13347,9963,21]),
[iquote('1:MRR:13347.0,13347.3,9963.0,21.0')] ).
cnf(13355,plain,
( ~ equal(u,sdtasdt0(xm,xm))
| equal(sdtasdt0(xm,xm),skc3) ),
inference(mrr,[status(thm)],[10588,13348]),
[iquote('1:MRR:10588.0,13348.1')] ).
cnf(13375,plain,
equal(sdtasdt0(xm,xm),skc3),
inference(aed,[status(thm),theory(equality)],[16,13355]),
[iquote('1:AED:16.0,13355.0')] ).
cnf(13386,plain,
equal(sdtasdt0(xm,xq),skc3),
inference(rew,[status(thm),theory(equality)],[13375,9982]),
[iquote('1:Rew:13375.0,9982.0')] ).
cnf(13428,plain,
( ~ equal(u,skc3)
| aNaturalNumber0(u) ),
inference(rew,[status(thm),theory(equality)],[13375,13348]),
[iquote('1:Rew:13375.0,13348.0')] ).
cnf(13706,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ equal(u,skc3)
| equal(xm,sz00)
| equal(sdtsldt0(u,xm),xm) ),
inference(spl,[status(thm),theory(equality)],[13375,106]),
[iquote('1:SpL:13375.0,106.3')] ).
cnf(13747,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ equal(u,skc3)
| equal(xm,sz00)
| equal(sdtsldt0(u,xm),xm) ),
inference(obv,[status(thm),theory(equality)],[13706]),
[iquote('1:Obv:13706.1')] ).
cnf(13833,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xq)
| ~ equal(u,skc3)
| equal(xm,sz00)
| equal(sdtsldt0(u,xm),xq) ),
inference(spl,[status(thm),theory(equality)],[13386,106]),
[iquote('1:SpL:13386.0,106.3')] ).
cnf(14630,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,skc3)
| equal(xm,sz00)
| equal(sdtsldt0(u,xm),xm) ),
inference(ssi,[status(thm)],[13747,4]),
[iquote('1:SSi:13747.1,4.0')] ).
cnf(14631,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,skc3)
| equal(sdtsldt0(u,xm),xm) ),
inference(mrr,[status(thm)],[14630,20]),
[iquote('1:MRR:14630.2,20.0')] ).
cnf(14632,plain,
( ~ equal(u,skc3)
| equal(sdtsldt0(u,xm),xm) ),
inference(mrr,[status(thm)],[14631,13428]),
[iquote('1:MRR:14631.0,13428.1')] ).
cnf(14644,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xq)
| ~ equal(u,skc3)
| equal(xm,sz00)
| equal(xq,xm) ),
inference(rew,[status(thm),theory(equality)],[14632,13833]),
[iquote('1:Rew:14632.1,13833.5')] ).
cnf(14645,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xq)
| ~ equal(u,skc3)
| equal(xm,sz00)
| equal(xq,xm) ),
inference(ssi,[status(thm)],[14644,4]),
[iquote('1:SSi:14644.1,4.0')] ).
cnf(14646,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xq)
| ~ equal(u,skc3)
| equal(xq,xm) ),
inference(mrr,[status(thm)],[14645,20]),
[iquote('1:MRR:14645.3,20.0')] ).
cnf(14647,plain,
( ~ equal(u,skc3)
| equal(xq,xm) ),
inference(mrr,[status(thm)],[14646,13428,9]),
[iquote('1:MRR:14646.0,14646.1,13428.1,9.0')] ).
cnf(15503,plain,
equal(xq,xm),
inference(aed,[status(thm),theory(equality)],[16,14647]),
[iquote('1:AED:16.0,14647.0')] ).
cnf(15524,plain,
equal(sdtasdt0(xp,xm),xm),
inference(rew,[status(thm),theory(equality)],[15503,9964]),
[iquote('1:Rew:15503.0,9964.0')] ).
cnf(15525,plain,
equal(sdtsldt0(xm,xp),xm),
inference(rew,[status(thm),theory(equality)],[15503,9965]),
[iquote('1:Rew:15503.0,9965.0')] ).
cnf(15526,plain,
( ~ equal(u,xm)
| aNaturalNumber0(u) ),
inference(rew,[status(thm),theory(equality)],[15503,3495]),
[iquote('1:Rew:15503.0,3495.0')] ).
cnf(15530,plain,
equal(sdtasdt0(xm,xp),xm),
inference(rew,[status(thm),theory(equality)],[15524,9986]),
[iquote('1:Rew:15524.0,9986.0')] ).
cnf(16008,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xm)
| equal(xm,sz00)
| equal(sdtsldt0(u,xm),xp) ),
inference(spl,[status(thm),theory(equality)],[15530,106]),
[iquote('1:SpL:15530.0,106.3')] ).
cnf(16018,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xm)
| equal(xm,sz00)
| equal(xp,sz10) ),
inference(rew,[status(thm),theory(equality)],[3854,16008]),
[iquote('1:Rew:3854.4,16008.5')] ).
cnf(16019,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm)
| equal(xm,sz00)
| equal(xp,sz10) ),
inference(ssi,[status(thm)],[16018,5,6,4]),
[iquote('1:SSi:16018.2,16018.1,5.0,6.0,4.0')] ).
cnf(16020,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xm) ),
inference(mrr,[status(thm)],[16019,20,22]),
[iquote('1:MRR:16019.2,16019.3,20.0,22.0')] ).
cnf(16021,plain,
~ equal(u,xm),
inference(mrr,[status(thm)],[16020,15526]),
[iquote('1:MRR:16020.0,15526.1')] ).
cnf(16022,plain,
$false,
inference(unc,[status(thm)],[16021,15525]),
[iquote('1:UnC:16021.0,15525.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM528+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jul 7 12:37:39 EDT 2022
% 0.11/0.33 % CPUTime :
% 5.75/5.90
% 5.75/5.90 SPASS V 3.9
% 5.75/5.90 SPASS beiseite: Proof found.
% 5.75/5.90 % SZS status Theorem
% 5.75/5.90 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.75/5.90 SPASS derived 9824 clauses, backtracked 2884 clauses, performed 25 splits and kept 5327 clauses.
% 5.75/5.90 SPASS allocated 109781 KBytes.
% 5.75/5.90 SPASS spent 0:00:05.56 on the problem.
% 5.75/5.90 0:00:00.04 for the input.
% 5.75/5.90 0:00:00.05 for the FLOTTER CNF translation.
% 5.75/5.90 0:00:00.09 for inferences.
% 5.75/5.90 0:00:00.06 for the backtracking.
% 5.75/5.90 0:00:05.27 for the reduction.
% 5.75/5.90
% 5.75/5.90
% 5.75/5.90 Here is a proof with depth 4, length 154 :
% 5.75/5.90 % SZS output start Refutation
% See solution above
% 6.66/6.90 Formulae used in the proof : mSortsC_01 m__2987 m__3025 m__3046 m__3059 mDefLE m_MulUnit m__3014 m__3082 m__3152 mSortsB_02 m__ mLETotal mMulComm mMonMul2 mLEAsym mDefDiv mMulAsso mDefQuot mDivAsso
% 6.66/6.90
%------------------------------------------------------------------------------