TSTP Solution File: NUM507+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM507+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 14:26:55 EDT 2022
% Result : Theorem 2.75s 2.92s
% Output : Refutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 34
% Syntax : Number of clauses : 125 ( 43 unt; 21 nHn; 125 RR)
% Number of literals : 357 ( 0 equ; 219 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aNaturalNumber0(sz00),
file('NUM507+1.p',unknown),
[] ).
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM507+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM507+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM507+1.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM507+1.p',unknown),
[] ).
cnf(7,axiom,
aNaturalNumber0(xr),
file('NUM507+1.p',unknown),
[] ).
cnf(8,axiom,
isPrime0(xr),
file('NUM507+1.p',unknown),
[] ).
cnf(14,axiom,
sdtlseqdt0(xr,xk),
file('NUM507+1.p',unknown),
[] ).
cnf(15,axiom,
sdtlseqdt0(xk,xp),
file('NUM507+1.p',unknown),
[] ).
cnf(16,axiom,
~ equal(sz10,sz00),
file('NUM507+1.p',unknown),
[] ).
cnf(17,axiom,
aNaturalNumber0(skf4(u,v)),
file('NUM507+1.p',unknown),
[] ).
cnf(25,axiom,
~ equal(xk,sz00),
file('NUM507+1.p',unknown),
[] ).
cnf(27,axiom,
~ equal(xk,xp),
file('NUM507+1.p',unknown),
[] ).
cnf(28,axiom,
doDivides0(xp,sdtasdt0(xn,xm)),
file('NUM507+1.p',unknown),
[] ).
cnf(29,axiom,
doDivides0(xr,sdtasdt0(xn,xm)),
file('NUM507+1.p',unknown),
[] ).
cnf(31,axiom,
equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk),
file('NUM507+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('NUM507+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM507+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM507+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ aNaturalNumber0(u)
| ~ isPrime0(u)
| ~ equal(u,sz00) ),
file('NUM507+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
file('NUM507+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
file('NUM507+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(v,sz00)
| sdtlseqdt0(u,sdtasdt0(u,v)) ),
file('NUM507+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| sdtlseqdt0(v,u)
| equal(u,sz00) ),
file('NUM507+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ sdtlseqdt0(u,v)
| equal(v,u) ),
file('NUM507+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM507+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM507+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,u)
| ~ sdtlseqdt0(w,v)
| sdtlseqdt0(w,u) ),
file('NUM507+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
file('NUM507+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM507+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(w,u)
| equal(w,u)
| sdtlseqdt0(sdtpldt0(v,w),sdtpldt0(v,u)) ),
file('NUM507+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('NUM507+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM507+1.p',unknown),
[] ).
cnf(86,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM507+1.p',unknown),
[] ).
cnf(94,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[86,62]),
[iquote('0:MRR:86.3,62.4')] ).
cnf(111,plain,
~ equal(xp,sz00),
inference(ems,[status(thm)],[40,5,6]),
[iquote('0:EmS:40.0,40.1,5.0,6.0')] ).
cnf(186,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(v,sz00)
| sdtlseqdt0(u,sdtasdt0(v,u)) ),
inference(spr,[status(thm),theory(equality)],[46,50]),
[iquote('0:SpR:46.2,50.3')] ).
cnf(191,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(v,sz00)
| sdtlseqdt0(u,sdtasdt0(v,u)) ),
inference(obv,[status(thm),theory(equality)],[186]),
[iquote('0:Obv:186.1')] ).
cnf(217,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| sdtlseqdt0(xr,sdtasdt0(xn,xm))
| equal(sdtasdt0(xn,xm),sz00) ),
inference(res,[status(thm),theory(equality)],[29,55]),
[iquote('0:Res:29.0,55.2')] ).
cnf(221,plain,
( sdtlseqdt0(xr,sdtasdt0(xn,xm))
| equal(sdtasdt0(xn,xm),sz00) ),
inference(ssi,[status(thm)],[217,8,7,39,3,4]),
[iquote('0:SSi:217.1,217.0,8.0,7.0,39.2,3.0,4.0')] ).
cnf(227,plain,
equal(sdtasdt0(xn,xm),sz00),
inference(spt,[spt(split,[position(s1)])],[221]),
[iquote('1:Spt:221.1')] ).
cnf(229,plain,
doDivides0(xp,sz00),
inference(rew,[status(thm),theory(equality)],[227,28]),
[iquote('1:Rew:227.0,28.0')] ).
cnf(230,plain,
equal(sdtsldt0(sz00,xp),xk),
inference(rew,[status(thm),theory(equality)],[227,31]),
[iquote('1:Rew:227.0,31.0')] ).
cnf(307,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(xk,xr)
| equal(xr,xk) ),
inference(res,[status(thm),theory(equality)],[14,59]),
[iquote('0:Res:14.0,59.2')] ).
cnf(319,plain,
( ~ aNaturalNumber0(xk)
| ~ sdtlseqdt0(xk,xr)
| equal(xr,xk) ),
inference(ssi,[status(thm)],[307,8,7]),
[iquote('0:SSi:307.1,8.0,7.0')] ).
cnf(398,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[62]),
[iquote('0:EqR:62.3')] ).
cnf(404,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| sdtlseqdt0(u,sdtpldt0(u,v)) ),
inference(ssi,[status(thm)],[398,38]),
[iquote('0:SSi:398.0,38.2')] ).
cnf(422,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(u)
| sdtlseqdt0(sz00,u) ),
inference(spr,[status(thm),theory(equality)],[33,404]),
[iquote('0:SpR:33.1,404.2')] ).
cnf(428,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(u)
| sdtlseqdt0(sz00,u) ),
inference(obv,[status(thm),theory(equality)],[422]),
[iquote('0:Obv:422.0')] ).
cnf(429,plain,
( ~ aNaturalNumber0(u)
| sdtlseqdt0(sz00,u) ),
inference(ssi,[status(thm)],[428,1]),
[iquote('0:SSi:428.0,1.0')] ).
cnf(436,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(u,sz00)
| equal(sz00,u) ),
inference(res,[status(thm),theory(equality)],[429,59]),
[iquote('0:Res:429.1,59.2')] ).
cnf(438,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(u,sz00)
| equal(sz00,u) ),
inference(obv,[status(thm),theory(equality)],[436]),
[iquote('0:Obv:436.0')] ).
cnf(439,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,sz00)
| equal(sz00,u) ),
inference(ssi,[status(thm)],[438,1]),
[iquote('0:SSi:438.1,1.0')] ).
cnf(792,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[94]),
[iquote('0:EqR:94.3')] ).
cnf(799,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[792,38]),
[iquote('0:SSi:792.0,38.2')] ).
cnf(812,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(u)
| equal(sdtmndt0(sdtpldt0(u,v),v),u) ),
inference(spr,[status(thm),theory(equality)],[45,799]),
[iquote('0:SpR:45.2,799.2')] ).
cnf(817,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,sdtpldt0(u,v))
| ~ equal(w,v)
| aNaturalNumber0(w) ),
inference(spl,[status(thm),theory(equality)],[799,63]),
[iquote('0:SpL:799.2,63.3')] ).
cnf(823,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(v,u),u),v) ),
inference(obv,[status(thm),theory(equality)],[812]),
[iquote('0:Obv:812.1')] ).
cnf(832,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(sdtpldt0(v,u))
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,sdtpldt0(v,u))
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(obv,[status(thm),theory(equality)],[817]),
[iquote('0:Obv:817.0')] ).
cnf(833,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,sdtpldt0(v,u))
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(ssi,[status(thm)],[832,38]),
[iquote('0:SSi:832.1,38.2')] ).
cnf(834,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ equal(w,u)
| aNaturalNumber0(w) ),
inference(mrr,[status(thm)],[833,404]),
[iquote('0:MRR:833.2,404.2')] ).
cnf(925,plain,
( ~ aNaturalNumber0(u)
| ~ equal(v,u)
| aNaturalNumber0(v) ),
inference(ems,[status(thm)],[834,17]),
[iquote('0:EmS:834.1,17.0')] ).
cnf(953,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(xk,xr)
| ~ equal(xk,u)
| equal(xr,xk) ),
inference(sor,[status(thm)],[319,925]),
[iquote('0:SoR:319.0,925.2')] ).
cnf(1166,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,xk)
| sdtlseqdt0(u,xp) ),
inference(res,[status(thm),theory(equality)],[15,67]),
[iquote('0:Res:15.0,67.3')] ).
cnf(1182,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,xk)
| sdtlseqdt0(u,xp) ),
inference(ssi,[status(thm)],[1166,6,5]),
[iquote('0:SSi:1166.0,6.0,5.0')] ).
cnf(1212,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(u,xk)
| ~ equal(xk,v)
| sdtlseqdt0(u,xp) ),
inference(sor,[status(thm)],[1182,925]),
[iquote('0:SoR:1182.0,925.2')] ).
cnf(1243,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sz00)
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[230,72]),
[iquote('1:SpL:230.0,72.3')] ).
cnf(1244,plain,
( ~ doDivides0(xp,sz00)
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[1243,6,5,1]),
[iquote('1:SSi:1243.1,1243.0,6.0,5.0,1.0')] ).
cnf(1245,plain,
( ~ equal(u,xk)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[1244,229,111]),
[iquote('1:MRR:1244.0,1244.3,229.0,111.0')] ).
cnf(2601,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sz00)
| ~ equal(u,xk)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),sz00) ),
inference(spl,[status(thm),theory(equality)],[230,83]),
[iquote('1:SpL:230.0,83.3')] ).
cnf(2602,plain,
( ~ doDivides0(xp,sz00)
| ~ equal(u,xk)
| equal(xp,sz00)
| equal(sdtasdt0(xp,u),sz00) ),
inference(ssi,[status(thm)],[2601,6,5,1]),
[iquote('1:SSi:2601.1,2601.0,6.0,5.0,1.0')] ).
cnf(2603,plain,
( ~ equal(u,xk)
| equal(sdtasdt0(xp,u),sz00) ),
inference(mrr,[status(thm)],[2602,229,111]),
[iquote('1:MRR:2602.0,2602.2,229.0,111.0')] ).
cnf(2606,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(xp)
| ~ equal(u,xk)
| equal(xp,sz00)
| sdtlseqdt0(u,sz00) ),
inference(spr,[status(thm),theory(equality)],[2603,191]),
[iquote('1:SpR:2603.1,191.3')] ).
cnf(2629,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xk)
| equal(xp,sz00)
| sdtlseqdt0(u,sz00) ),
inference(ssi,[status(thm)],[2606,6,5]),
[iquote('1:SSi:2606.1,6.0,5.0')] ).
cnf(2630,plain,
( ~ equal(u,xk)
| sdtlseqdt0(u,sz00) ),
inference(mrr,[status(thm)],[2629,1245,111]),
[iquote('1:MRR:2629.0,2629.2,1245.1,111.0')] ).
cnf(2645,plain,
( ~ aNaturalNumber0(u)
| ~ equal(u,xk)
| equal(sz00,u) ),
inference(res,[status(thm),theory(equality)],[2630,439]),
[iquote('1:Res:2630.1,439.1')] ).
cnf(2655,plain,
( ~ equal(u,xk)
| equal(sz00,u) ),
inference(mrr,[status(thm)],[2645,1245]),
[iquote('1:MRR:2645.0,1245.1')] ).
cnf(2876,plain,
equal(xk,sz00),
inference(eqr,[status(thm),theory(equality)],[2655]),
[iquote('1:EqR:2655.0')] ).
cnf(2877,plain,
$false,
inference(mrr,[status(thm)],[2876,25]),
[iquote('1:MRR:2876.0,25.0')] ).
cnf(2878,plain,
~ equal(sdtasdt0(xn,xm),sz00),
inference(spt,[spt(split,[position(sa)])],[2877,227]),
[iquote('1:Spt:2877.0,221.1,227.0')] ).
cnf(2879,plain,
sdtlseqdt0(xr,sdtasdt0(xn,xm)),
inference(spt,[spt(split,[position(s2)])],[221]),
[iquote('1:Spt:2877.0,221.0')] ).
cnf(2925,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(spl,[status(thm),theory(equality)],[31,72]),
[iquote('0:SpL:31.0,72.3')] ).
cnf(2926,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ equal(u,xk)
| aNaturalNumber0(u)
| equal(xp,sz00) ),
inference(ssi,[status(thm)],[2925,6,5,39,3,4]),
[iquote('0:SSi:2925.1,2925.0,6.0,5.0,39.2,3.0,4.0')] ).
cnf(2927,plain,
( ~ equal(u,xk)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[2926,28,111]),
[iquote('0:MRR:2926.0,2926.3,28.0,111.0')] ).
cnf(2929,plain,
( ~ sdtlseqdt0(xk,xr)
| ~ equal(xk,u)
| equal(xr,xk) ),
inference(mrr,[status(thm)],[953,2927]),
[iquote('0:MRR:953.0,2927.1')] ).
cnf(2931,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,xk)
| ~ equal(xk,v)
| sdtlseqdt0(u,xp) ),
inference(mrr,[status(thm)],[1212,2927]),
[iquote('0:MRR:1212.1,2927.1')] ).
cnf(2934,plain,
( ~ sdtlseqdt0(xk,xr)
| equal(xr,xk) ),
inference(aed,[status(thm),theory(equality)],[16,2929]),
[iquote('0:AED:16.0,2929.1')] ).
cnf(2936,plain,
( ~ aNaturalNumber0(u)
| ~ sdtlseqdt0(u,xk)
| sdtlseqdt0(u,xp) ),
inference(aed,[status(thm),theory(equality)],[16,2931]),
[iquote('0:AED:16.0,2931.2')] ).
cnf(2958,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(xr,xp)
| equal(xr,xp)
| equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(res,[status(thm),theory(equality)],[79,82]),
[iquote('0:Res:79.5,82.0')] ).
cnf(2960,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(xr,xp)
| equal(xr,xp)
| equal(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(rew,[status(thm),theory(equality)],[45,2958]),
[iquote('0:Rew:45.2,2958.5,45.2,2958.5')] ).
cnf(2961,plain,
( ~ sdtlseqdt0(xr,xp)
| equal(xr,xp)
| equal(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(ssi,[status(thm)],[2960,7,8,38,3,4,6,5]),
[iquote('0:SSi:2960.2,2960.1,2960.0,7.0,8.0,38.0,3.0,4.2,6.0,5.0')] ).
cnf(3291,plain,
( ~ aNaturalNumber0(xr)
| sdtlseqdt0(xr,xp) ),
inference(res,[status(thm),theory(equality)],[14,2936]),
[iquote('0:Res:14.0,2936.1')] ).
cnf(3296,plain,
sdtlseqdt0(xr,xp),
inference(ssi,[status(thm)],[3291,7,8]),
[iquote('0:SSi:3291.0,7.0,8.0')] ).
cnf(3297,plain,
( equal(xr,xp)
| equal(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(mrr,[status(thm)],[2961,3296]),
[iquote('0:MRR:2961.0,3296.0')] ).
cnf(3688,plain,
equal(xr,xp),
inference(spt,[spt(split,[position(s2s1)])],[3297]),
[iquote('2:Spt:3297.0')] ).
cnf(3698,plain,
( ~ sdtlseqdt0(xk,xp)
| equal(xr,xk) ),
inference(rew,[status(thm),theory(equality)],[3688,2934]),
[iquote('2:Rew:3688.0,2934.0')] ).
cnf(3733,plain,
( ~ sdtlseqdt0(xk,xp)
| equal(xk,xp) ),
inference(rew,[status(thm),theory(equality)],[3688,3698]),
[iquote('2:Rew:3688.0,3698.1')] ).
cnf(3734,plain,
$false,
inference(mrr,[status(thm)],[3733,15,27]),
[iquote('2:MRR:3733.0,3733.1,15.0,27.0')] ).
cnf(3746,plain,
~ equal(xr,xp),
inference(spt,[spt(split,[position(s2sa)])],[3734,3688]),
[iquote('2:Spt:3734.0,3297.0,3688.0')] ).
cnf(3747,plain,
equal(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm))),
inference(spt,[spt(split,[position(s2s2)])],[3297]),
[iquote('2:Spt:3734.0,3297.1')] ).
cnf(3753,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr)
| equal(sdtmndt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,xm)),xr) ),
inference(spr,[status(thm),theory(equality)],[3747,823]),
[iquote('2:SpR:3747.0,823.2')] ).
cnf(3782,plain,
( ~ aNaturalNumber0(xr)
| equal(sdtmndt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,xm)),xr) ),
inference(ssi,[status(thm)],[3753,38,3,4]),
[iquote('2:SSi:3753.0,38.0,3.0,4.2')] ).
cnf(3783,plain,
equal(sdtmndt0(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,xm)),xr),
inference(mrr,[status(thm)],[3782,7]),
[iquote('2:MRR:3782.0,7.0')] ).
cnf(3856,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(spt,[spt(split,[position(s2s2s1)])],[82]),
[iquote('3:Spt:82.0')] ).
cnf(3868,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr)
| ~ sdtlseqdt0(xr,xp)
| equal(xr,xp) ),
inference(res,[status(thm),theory(equality)],[79,3856]),
[iquote('3:Res:79.5,3856.0')] ).
cnf(3870,plain,
( ~ sdtlseqdt0(xr,xp)
| equal(xr,xp) ),
inference(ssi,[status(thm)],[3868,8,7,38,3,4,6,5]),
[iquote('3:SSi:3868.2,3868.1,3868.0,8.0,7.0,38.0,3.0,4.2,6.0,5.0')] ).
cnf(3871,plain,
$false,
inference(mrr,[status(thm)],[3870,3296,3746]),
[iquote('3:MRR:3870.0,3870.1,3296.0,3746.0')] ).
cnf(3880,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(spt,[spt(split,[position(s2s2sa)])],[3871,3856]),
[iquote('3:Spt:3871.0,82.0,3856.0')] ).
cnf(3881,plain,
equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(spt,[spt(split,[position(s2s2s2)])],[82]),
[iquote('3:Spt:3871.0,82.1')] ).
cnf(3886,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xn,xm))) ),
inference(spr,[status(thm),theory(equality)],[3881,45]),
[iquote('3:SpR:3881.0,45.2')] ).
cnf(3893,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(spr,[status(thm),theory(equality)],[3881,71]),
[iquote('3:SpR:3881.0,71.3')] ).
cnf(3915,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xp,sdtpldt0(xn,xm))) ),
inference(rew,[status(thm),theory(equality)],[3747,3886]),
[iquote('3:Rew:3747.0,3886.2')] ).
cnf(3916,plain,
equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xp,sdtpldt0(xn,xm))),
inference(ssi,[status(thm)],[3915,38,3,4,8,7]),
[iquote('3:SSi:3915.1,3915.0,38.0,3.0,4.0,8.0,7.2')] ).
cnf(3940,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| equal(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,sdtpldt0(xm,xr))) ),
inference(rew,[status(thm),theory(equality)],[3916,3893]),
[iquote('3:Rew:3916.0,3893.3')] ).
cnf(3941,plain,
equal(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,sdtpldt0(xm,xr))),
inference(ssi,[status(thm)],[3940,3,4,8,7]),
[iquote('3:SSi:3940.2,3940.1,3940.0,3.0,4.0,8.0,7.0')] ).
cnf(3947,plain,
equal(sdtmndt0(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(xn,xm)),xr),
inference(rew,[status(thm),theory(equality)],[3941,3783]),
[iquote('3:Rew:3941.0,3783.0')] ).
cnf(3963,plain,
equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr))),
inference(rew,[status(thm),theory(equality)],[3941,3916]),
[iquote('3:Rew:3941.0,3916.0')] ).
cnf(9253,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| equal(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(spr,[status(thm),theory(equality)],[3963,71]),
[iquote('3:SpR:3963.0,71.3')] ).
cnf(9271,plain,
equal(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(xn,sdtpldt0(xm,xp))),
inference(ssi,[status(thm)],[9253,3,4,6,5]),
[iquote('3:SSi:9253.2,9253.1,9253.0,3.0,4.0,6.0,5.0')] ).
cnf(9280,plain,
equal(sdtmndt0(sdtpldt0(xn,sdtpldt0(xm,xp)),sdtpldt0(xn,xm)),xr),
inference(rew,[status(thm),theory(equality)],[9271,3947]),
[iquote('3:Rew:9271.0,3947.0')] ).
cnf(9286,plain,
equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp))),
inference(rew,[status(thm),theory(equality)],[9271,3963]),
[iquote('3:Rew:9271.0,3963.0')] ).
cnf(9775,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| equal(sdtmndt0(sdtpldt0(xn,sdtpldt0(xm,xp)),sdtpldt0(xn,xm)),xp) ),
inference(spr,[status(thm),theory(equality)],[9286,799]),
[iquote('3:SpR:9286.0,799.2')] ).
cnf(9783,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| equal(xr,xp) ),
inference(rew,[status(thm),theory(equality)],[9280,9775]),
[iquote('3:Rew:9280.0,9775.2')] ).
cnf(9784,plain,
equal(xr,xp),
inference(ssi,[status(thm)],[9783,6,5,38,3,4]),
[iquote('3:SSi:9783.1,9783.0,6.0,5.0,38.2,3.0,4.0')] ).
cnf(9785,plain,
$false,
inference(mrr,[status(thm)],[9784,3746]),
[iquote('3:MRR:9784.0,3746.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM507+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 : Tue Jul 5 21:27:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.75/2.92
% 2.75/2.92 SPASS V 3.9
% 2.75/2.92 SPASS beiseite: Proof found.
% 2.75/2.92 % SZS status Theorem
% 2.75/2.92 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.75/2.92 SPASS derived 6140 clauses, backtracked 1270 clauses, performed 16 splits and kept 3285 clauses.
% 2.75/2.92 SPASS allocated 105565 KBytes.
% 2.75/2.92 SPASS spent 0:00:02.58 on the problem.
% 2.75/2.92 0:00:00.04 for the input.
% 2.75/2.92 0:00:00.04 for the FLOTTER CNF translation.
% 2.75/2.92 0:00:00.07 for inferences.
% 2.75/2.92 0:00:00.02 for the backtracking.
% 2.75/2.92 0:00:02.36 for the reduction.
% 2.75/2.92
% 2.75/2.92
% 2.75/2.92 Here is a proof with depth 5, length 125 :
% 2.75/2.92 % SZS output start Refutation
% See solution above
% 3.24/3.40 Formulae used in the proof : mSortsC m__1837 m__1860 m__2342 m__2362 m__2377 mSortsC_01 mDefLE m__2327 m__2306 m_AddZero mSortsB mSortsB_02 mDefPrime mAddComm mMulComm mMonMul2 mDivLE mLEAsym mDefDiff mLETran mAddAsso mDefQuot mMonAdd m__
% 3.24/3.40
%------------------------------------------------------------------------------