TSTP Solution File: RNG081+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG081+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 20:41:25 EDT 2022
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 14 unt; 1 nHn; 36 RR)
% Number of literals : 77 ( 0 equ; 55 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
aScalar0(sz0z00),
file('RNG081+1.p',unknown),
[] ).
cnf(3,axiom,
aVector0(xs),
file('RNG081+1.p',unknown),
[] ).
cnf(4,axiom,
aVector0(xt),
file('RNG081+1.p',unknown),
[] ).
cnf(7,axiom,
equal(aDimensionOf0(xt),aDimensionOf0(xs)),
file('RNG081+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ aScalar0(u)
| equal(sdtasdt0(u,sz0z00),sz0z00) ),
file('RNG081+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ aScalar0(u)
| equal(sdtasdt0(sz0z00,u),sz0z00) ),
file('RNG081+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ aVector0(u)
| sdtlseqdt0(sz0z00,sdtasasdt0(u,u)) ),
file('RNG081+1.p',unknown),
[] ).
cnf(46,axiom,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
file('RNG081+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ aVector0(u)
| ~ aVector0(v)
| ~ equal(aDimensionOf0(v),aDimensionOf0(u))
| aScalar0(sdtasasdt0(v,u)) ),
file('RNG081+1.p',unknown),
[] ).
cnf(50,axiom,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| equal(aDimensionOf0(xs),sz00) ),
file('RNG081+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ aVector0(u)
| ~ aVector0(v)
| ~ equal(aDimensionOf0(u),sz00)
| ~ equal(aDimensionOf0(v),aDimensionOf0(u))
| equal(sdtasasdt0(v,u),sz0z00) ),
file('RNG081+1.p',unknown),
[] ).
cnf(78,plain,
equal(aDimensionOf0(xs),sz00),
inference(mrr,[status(thm)],[50,46]),
[iquote('0:MRR:50.0,46.0')] ).
cnf(79,plain,
equal(aDimensionOf0(xt),sz00),
inference(rew,[status(thm),theory(equality)],[78,7]),
[iquote('0:Rew:78.0,7.0')] ).
cnf(82,plain,
( ~ aVector0(u)
| ~ aVector0(xt)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xt))
| equal(sdtasasdt0(u,xt),sz0z00) ),
inference(res,[status(thm),theory(equality)],[79,59]),
[iquote('0:Res:79.0,59.2')] ).
cnf(95,plain,
( ~ aVector0(u)
| ~ aVector0(xt)
| ~ equal(aDimensionOf0(u),sz00)
| equal(sdtasasdt0(u,xt),sz0z00) ),
inference(rew,[status(thm),theory(equality)],[79,82]),
[iquote('0:Rew:79.0,82.2')] ).
cnf(96,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),sz00)
| equal(sdtasasdt0(u,xt),sz0z00) ),
inference(mrr,[status(thm)],[95,4]),
[iquote('0:MRR:95.1,4.0')] ).
cnf(155,plain,
( ~ aVector0(xt)
| ~ aVector0(xt)
| ~ equal(aDimensionOf0(xt),sz00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(spr,[status(thm),theory(equality)],[96,23]),
[iquote('0:SpR:96.2,23.1')] ).
cnf(157,plain,
( ~ aVector0(xt)
| ~ equal(aDimensionOf0(xt),sz00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(obv,[status(thm),theory(equality)],[155]),
[iquote('0:Obv:155.0')] ).
cnf(158,plain,
( ~ aVector0(xt)
| ~ equal(sz00,sz00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(rew,[status(thm),theory(equality)],[79,157]),
[iquote('0:Rew:79.0,157.1')] ).
cnf(159,plain,
( ~ aVector0(xt)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(obv,[status(thm),theory(equality)],[158]),
[iquote('0:Obv:158.1')] ).
cnf(160,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(ssi,[status(thm)],[159,4]),
[iquote('0:SSi:159.0,4.0')] ).
cnf(496,plain,
( ~ aVector0(xs)
| ~ equal(aDimensionOf0(xs),sz00)
| ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(spl,[status(thm),theory(equality)],[96,46]),
[iquote('0:SpL:96.2,46.0')] ).
cnf(501,plain,
( ~ aVector0(xs)
| ~ equal(sz00,sz00)
| ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(rew,[status(thm),theory(equality)],[78,496]),
[iquote('0:Rew:78.0,496.1')] ).
cnf(502,plain,
( ~ aVector0(xs)
| ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(obv,[status(thm),theory(equality)],[501]),
[iquote('0:Obv:501.1')] ).
cnf(503,plain,
~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(ssi,[status(thm)],[502,3]),
[iquote('0:SSi:502.0,3.0')] ).
cnf(514,plain,
( ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(spl,[status(thm),theory(equality)],[20,503]),
[iquote('0:SpL:20.1,503.0')] ).
cnf(518,plain,
~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(ssi,[status(thm)],[514,2]),
[iquote('0:SSi:514.0,2.0')] ).
cnf(527,plain,
( ~ aVector0(xt)
| ~ equal(aDimensionOf0(xt),sz00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
inference(spl,[status(thm),theory(equality)],[96,518]),
[iquote('0:SpL:96.2,518.0')] ).
cnf(529,plain,
( ~ aVector0(xt)
| ~ equal(sz00,sz00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
inference(rew,[status(thm),theory(equality)],[79,527]),
[iquote('0:Rew:79.0,527.1')] ).
cnf(530,plain,
( ~ aVector0(xt)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
inference(obv,[status(thm),theory(equality)],[529]),
[iquote('0:Obv:529.1')] ).
cnf(531,plain,
~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)),
inference(ssi,[status(thm)],[530,4]),
[iquote('0:SSi:530.0,4.0')] ).
cnf(537,plain,
( ~ aScalar0(sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sz0z00) ),
inference(spl,[status(thm),theory(equality)],[19,531]),
[iquote('0:SpL:19.1,531.0')] ).
cnf(539,plain,
~ aScalar0(sdtasasdt0(xs,xs)),
inference(mrr,[status(thm)],[537,160]),
[iquote('0:MRR:537.1,160.0')] ).
cnf(543,plain,
( ~ aVector0(xs)
| ~ aVector0(xs)
| ~ equal(aDimensionOf0(xs),aDimensionOf0(xs)) ),
inference(sor,[status(thm)],[539,47]),
[iquote('0:SoR:539.0,47.3')] ).
cnf(546,plain,
~ aVector0(xs),
inference(obv,[status(thm),theory(equality)],[543]),
[iquote('0:Obv:543.2')] ).
cnf(547,plain,
$false,
inference(ssi,[status(thm)],[546,3]),
[iquote('0:SSi:546.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : RNG081+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 : Mon May 30 09:10:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.17/0.47
% 0.17/0.47 SPASS V 3.9
% 0.17/0.47 SPASS beiseite: Proof found.
% 0.17/0.47 % SZS status Theorem
% 0.17/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 SPASS derived 237 clauses, backtracked 0 clauses, performed 0 splits and kept 116 clauses.
% 0.17/0.47 SPASS allocated 98155 KBytes.
% 0.17/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.17/0.47 0:00:00.04 for the input.
% 0.17/0.47 0:00:00.04 for the FLOTTER CNF translation.
% 0.17/0.47 0:00:00.00 for inferences.
% 0.17/0.47 0:00:00.00 for the backtracking.
% 0.17/0.47 0:00:00.02 for the reduction.
% 0.17/0.47
% 0.17/0.47
% 0.17/0.47 Here is a proof with depth 6, length 36 :
% 0.17/0.47 % SZS output start Refutation
% See solution above
% 0.17/0.47 Formulae used in the proof : mSZeroSc m__1678 m__1678_01 mScZero mScSqPos m__ mScPr mDefSPZ
% 0.17/0.47
%------------------------------------------------------------------------------