TSTP Solution File: NUM475+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM475+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:26:34 EDT 2022
% Result : Theorem 0.92s 1.12s
% Output : Refutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of clauses : 45 ( 17 unt; 8 nHn; 45 RR)
% Number of literals : 125 ( 0 equ; 74 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xl),
file('NUM475+1.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM475+1.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xn),
file('NUM475+1.p',unknown),
[] ).
cnf(6,axiom,
doDivides0(xl,xm),
file('NUM475+1.p',unknown),
[] ).
cnf(7,axiom,
sdtlseqdt0(xp,xq),
file('NUM475+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(xl,sz00),
file('NUM475+1.p',unknown),
[] ).
cnf(12,axiom,
doDivides0(xl,sdtpldt0(xm,xn)),
file('NUM475+1.p',unknown),
[] ).
cnf(13,axiom,
equal(sdtsldt0(xm,xl),xp),
file('NUM475+1.p',unknown),
[] ).
cnf(14,axiom,
equal(sdtmndt0(xq,xp),xr),
file('NUM475+1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(sdtasdt0(xl,xr),xn),
file('NUM475+1.p',unknown),
[] ).
cnf(17,axiom,
equal(sdtsldt0(sdtpldt0(xm,xn),xl),xq),
file('NUM475+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM475+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM475+1.p',unknown),
[] ).
cnf(32,axiom,
equal(sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)),sdtpldt0(sdtasdt0(xl,xp),xn)),
file('NUM475+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM475+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| ~ equal(w,sdtmndt0(u,v))
| aNaturalNumber0(w) ),
file('NUM475+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| aNaturalNumber0(w)
| equal(v,sz00) ),
file('NUM475+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ doDivides0(v,u)
| ~ equal(w,sdtsldt0(u,v))
| equal(v,sz00)
| equal(u,sdtasdt0(v,w)) ),
file('NUM475+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM475+1.p',unknown),
[] ).
cnf(68,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[62,41]),
[iquote('0:MRR:62.3,41.4')] ).
cnf(479,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ sdtlseqdt0(v,u)
| aNaturalNumber0(sdtmndt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[42]),
[iquote('0:EqR:42.3')] ).
cnf(652,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xp,xq)
| aNaturalNumber0(xr) ),
inference(spr,[status(thm),theory(equality)],[14,479]),
[iquote('0:SpR:14.0,479.3')] ).
cnf(653,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(xr) ),
inference(mrr,[status(thm)],[652,7]),
[iquote('0:MRR:652.2,7.0')] ).
cnf(656,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[68]),
[iquote('0:EqR:68.3')] ).
cnf(664,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[656,24]),
[iquote('0:SSi:656.0,24.2')] ).
cnf(1047,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ~ equal(u,xp)
| aNaturalNumber0(u)
| equal(xl,sz00) ),
inference(spl,[status(thm),theory(equality)],[13,50]),
[iquote('0:SpL:13.0,50.3')] ).
cnf(1048,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ equal(u,xq)
| aNaturalNumber0(u)
| equal(xl,sz00) ),
inference(spl,[status(thm),theory(equality)],[17,50]),
[iquote('0:SpL:17.0,50.3')] ).
cnf(1049,plain,
( ~ doDivides0(xl,xm)
| ~ equal(u,xp)
| aNaturalNumber0(u)
| equal(xl,sz00) ),
inference(ssi,[status(thm)],[1047,3,4]),
[iquote('0:SSi:1047.1,1047.0,3.0,4.0')] ).
cnf(1050,plain,
( ~ equal(u,xp)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[1049,6,11]),
[iquote('0:MRR:1049.0,1049.3,6.0,11.0')] ).
cnf(1051,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ equal(u,xq)
| aNaturalNumber0(u)
| equal(xl,sz00) ),
inference(ssi,[status(thm)],[1048,3,24,4,5]),
[iquote('0:SSi:1048.1,1048.0,3.0,24.0,4.2,5.0')] ).
cnf(1052,plain,
( ~ equal(u,xq)
| aNaturalNumber0(u) ),
inference(mrr,[status(thm)],[1051,12,11]),
[iquote('0:MRR:1051.0,1051.3,12.0,11.0')] ).
cnf(1074,plain,
( ~ aNaturalNumber0(xq)
| ~ equal(xp,xp)
| aNaturalNumber0(xr) ),
inference(sor,[status(thm)],[653,1050]),
[iquote('0:SoR:653.1,1050.1')] ).
cnf(1083,plain,
( ~ aNaturalNumber0(xq)
| aNaturalNumber0(xr) ),
inference(obv,[status(thm),theory(equality)],[1074]),
[iquote('0:Obv:1074.1')] ).
cnf(1160,plain,
( ~ equal(xq,xq)
| aNaturalNumber0(xr) ),
inference(sor,[status(thm)],[1083,1052]),
[iquote('0:SoR:1083.0,1052.1')] ).
cnf(1161,plain,
aNaturalNumber0(xr),
inference(obv,[status(thm),theory(equality)],[1160]),
[iquote('0:Obv:1160.0')] ).
cnf(2154,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ~ equal(u,xp)
| equal(xl,sz00)
| equal(sdtasdt0(xl,u),xm) ),
inference(spl,[status(thm),theory(equality)],[13,59]),
[iquote('0:SpL:13.0,59.3')] ).
cnf(2156,plain,
( ~ doDivides0(xl,xm)
| ~ equal(u,xp)
| equal(xl,sz00)
| equal(sdtasdt0(xl,u),xm) ),
inference(ssi,[status(thm)],[2154,3,4]),
[iquote('0:SSi:2154.1,2154.0,3.0,4.0')] ).
cnf(2157,plain,
( ~ equal(u,xp)
| equal(sdtasdt0(xl,u),xm) ),
inference(mrr,[status(thm)],[2156,6,11]),
[iquote('0:MRR:2156.0,2156.2,6.0,11.0')] ).
cnf(2520,plain,
( ~ equal(xp,xp)
| equal(sdtpldt0(xm,sdtasdt0(xl,xr)),sdtpldt0(xm,xn)) ),
inference(spr,[status(thm),theory(equality)],[2157,32]),
[iquote('0:SpR:2157.1,32.0')] ).
cnf(2535,plain,
equal(sdtpldt0(xm,sdtasdt0(xl,xr)),sdtpldt0(xm,xn)),
inference(obv,[status(thm),theory(equality)],[2520]),
[iquote('0:Obv:2520.0')] ).
cnf(2651,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| equal(sdtmndt0(sdtpldt0(xm,xn),xm),sdtasdt0(xl,xr)) ),
inference(spr,[status(thm),theory(equality)],[2535,664]),
[iquote('0:SpR:2535.0,664.2')] ).
cnf(2669,plain,
equal(sdtmndt0(sdtpldt0(xm,xn),xm),sdtasdt0(xl,xr)),
inference(ssi,[status(thm)],[2651,25,3,1161,4]),
[iquote('0:SSi:2651.1,2651.0,25.0,3.0,1161.0,4.2')] ).
cnf(2752,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| equal(sdtasdt0(xl,xr),xn) ),
inference(spr,[status(thm),theory(equality)],[2669,664]),
[iquote('0:SpR:2669.0,664.2')] ).
cnf(2757,plain,
equal(sdtasdt0(xl,xr),xn),
inference(ssi,[status(thm)],[2752,5,4]),
[iquote('0:SSi:2752.1,2752.0,5.0,4.0')] ).
cnf(2758,plain,
$false,
inference(mrr,[status(thm)],[2757,15]),
[iquote('0:MRR:2757.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : NUM475+1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n020.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Tue Jul 5 15:31:44 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.92/1.12
% 0.92/1.12 SPASS V 3.9
% 0.92/1.12 SPASS beiseite: Proof found.
% 0.92/1.12 % SZS status Theorem
% 0.92/1.12 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.92/1.12 SPASS derived 1640 clauses, backtracked 79 clauses, performed 1 splits and kept 805 clauses.
% 0.92/1.12 SPASS allocated 100240 KBytes.
% 0.92/1.12 SPASS spent 0:00:00.77 on the problem.
% 0.92/1.12 0:00:00.03 for the input.
% 0.92/1.12 0:00:00.03 for the FLOTTER CNF translation.
% 0.92/1.12 0:00:00.03 for inferences.
% 0.92/1.12 0:00:00.00 for the backtracking.
% 0.92/1.12 0:00:00.65 for the reduction.
% 0.92/1.12
% 0.92/1.12
% 0.92/1.12 Here is a proof with depth 4, length 45 :
% 0.92/1.12 % SZS output start Refutation
% See solution above
% 0.92/1.12 Formulae used in the proof : m__1324 m__1324_04 m__1395 m__1347 m__1360 m__1422 m__ m__1379 mSortsB mSortsB_02 m__1459 mDefLE mDefDiff mDefQuot
% 0.92/1.12
%------------------------------------------------------------------------------