TSTP Solution File: NUM475+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM475+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:26:35 EDT 2022
% Result : Theorem 1.13s 1.31s
% Output : Refutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 21 ( 11 unt; 0 nHn; 21 RR)
% Number of literals : 48 ( 0 equ; 31 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xl),
file('NUM475+2.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM475+2.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xn),
file('NUM475+2.p',unknown),
[] ).
cnf(11,axiom,
aNaturalNumber0(xr),
file('NUM475+2.p',unknown),
[] ).
cnf(20,axiom,
equal(sdtasdt0(xl,xp),xm),
file('NUM475+2.p',unknown),
[] ).
cnf(25,axiom,
~ equal(sdtasdt0(xl,xr),xn),
file('NUM475+2.p',unknown),
[] ).
cnf(36,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtpldt0(v,u)) ),
file('NUM475+2.p',unknown),
[] ).
cnf(37,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM475+2.p',unknown),
[] ).
cnf(44,axiom,
equal(sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)),sdtpldt0(sdtasdt0(xl,xp),xn)),
file('NUM475+2.p',unknown),
[] ).
cnf(53,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| sdtlseqdt0(v,u) ),
file('NUM475+2.p',unknown),
[] ).
cnf(74,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ sdtlseqdt0(v,w)
| ~ equal(sdtpldt0(v,u),w)
| equal(u,sdtmndt0(w,v)) ),
file('NUM475+2.p',unknown),
[] ).
cnf(80,plain,
equal(sdtpldt0(xm,sdtasdt0(xl,xr)),sdtpldt0(xm,xn)),
inference(rew,[status(thm),theory(equality)],[20,44]),
[iquote('0:Rew:20.0,44.0')] ).
cnf(81,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(sdtpldt0(v,w),u)
| equal(w,sdtmndt0(u,v)) ),
inference(mrr,[status(thm)],[74,53]),
[iquote('0:MRR:74.3,53.4')] ).
cnf(1007,plain,
( ~ aNaturalNumber0(sdtpldt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(eqr,[status(thm),theory(equality)],[81]),
[iquote('0:EqR:81.3')] ).
cnf(1019,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| equal(sdtmndt0(sdtpldt0(u,v),u),v) ),
inference(ssi,[status(thm)],[1007,36]),
[iquote('0:SSi:1007.0,36.2')] ).
cnf(4055,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| equal(sdtasdt0(xl,xr),sdtmndt0(sdtpldt0(xm,xn),xm)) ),
inference(spr,[status(thm),theory(equality)],[80,1019]),
[iquote('0:SpR:80.0,1019.2')] ).
cnf(4071,plain,
equal(sdtasdt0(xl,xr),sdtmndt0(sdtpldt0(xm,xn),xm)),
inference(ssi,[status(thm)],[4055,37,3,11,4]),
[iquote('0:SSi:4055.1,4055.0,37.0,3.0,11.0,4.2')] ).
cnf(4072,plain,
~ equal(sdtmndt0(sdtpldt0(xm,xn),xm),xn),
inference(rew,[status(thm),theory(equality)],[4071,25]),
[iquote('0:Rew:4071.0,25.0')] ).
cnf(4139,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ equal(xn,xn) ),
inference(spl,[status(thm),theory(equality)],[1019,4072]),
[iquote('0:SpL:1019.2,4072.0')] ).
cnf(4140,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(obv,[status(thm),theory(equality)],[4139]),
[iquote('0:Obv:4139.2')] ).
cnf(4141,plain,
$false,
inference(ssi,[status(thm)],[4140,5,4]),
[iquote('0:SSi:4140.1,4140.0,5.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM475+2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.32 % Computer : n025.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Thu Jul 7 07:21:13 EDT 2022
% 0.13/0.32 % CPUTime :
% 1.13/1.31
% 1.13/1.31 SPASS V 3.9
% 1.13/1.31 SPASS beiseite: Proof found.
% 1.13/1.31 % SZS status Theorem
% 1.13/1.31 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.13/1.31 SPASS derived 2665 clauses, backtracked 92 clauses, performed 5 splits and kept 1159 clauses.
% 1.13/1.31 SPASS allocated 101305 KBytes.
% 1.13/1.31 SPASS spent 0:00:00.93 on the problem.
% 1.13/1.31 0:00:00.04 for the input.
% 1.13/1.31 0:00:00.04 for the FLOTTER CNF translation.
% 1.13/1.31 0:00:00.03 for inferences.
% 1.13/1.31 0:00:00.00 for the backtracking.
% 1.13/1.31 0:00:00.78 for the reduction.
% 1.13/1.31
% 1.13/1.31
% 1.13/1.31 Here is a proof with depth 2, length 21 :
% 1.13/1.31 % SZS output start Refutation
% See solution above
% 1.13/1.31 Formulae used in the proof : m__1324 m__1422 m__1360 m__ mSortsB mSortsB_02 m__1459 mDefLE mDefDiff
% 1.13/1.31
%------------------------------------------------------------------------------