TSTP Solution File: RNG081+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 0.20s 0.50s
% Output : Refutation 0.20s
% 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+2.p',unknown),
[] ).
cnf(3,axiom,
aVector0(xs),
file('RNG081+2.p',unknown),
[] ).
cnf(4,axiom,
aVector0(xt),
file('RNG081+2.p',unknown),
[] ).
cnf(7,axiom,
equal(aDimensionOf0(xt),aDimensionOf0(xs)),
file('RNG081+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ aScalar0(u)
| equal(sdtasdt0(u,sz0z00),sz0z00) ),
file('RNG081+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ aScalar0(u)
| equal(sdtasdt0(sz0z00,u),sz0z00) ),
file('RNG081+2.p',unknown),
[] ).
cnf(23,axiom,
( ~ aVector0(u)
| sdtlseqdt0(sz0z00,sdtasasdt0(u,u)) ),
file('RNG081+2.p',unknown),
[] ).
cnf(50,axiom,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
file('RNG081+2.p',unknown),
[] ).
cnf(51,axiom,
( ~ aVector0(u)
| ~ aVector0(v)
| ~ equal(aDimensionOf0(v),aDimensionOf0(u))
| aScalar0(sdtasasdt0(v,u)) ),
file('RNG081+2.p',unknown),
[] ).
cnf(54,axiom,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| equal(aDimensionOf0(xs),sz00) ),
file('RNG081+2.p',unknown),
[] ).
cnf(63,axiom,
( ~ aVector0(u)
| ~ aVector0(v)
| ~ equal(aDimensionOf0(u),sz00)
| ~ equal(aDimensionOf0(v),aDimensionOf0(u))
| equal(sdtasasdt0(v,u),sz0z00) ),
file('RNG081+2.p',unknown),
[] ).
cnf(83,plain,
equal(aDimensionOf0(xs),sz00),
inference(mrr,[status(thm)],[54,50]),
[iquote('0:MRR:54.0,50.0')] ).
cnf(84,plain,
equal(aDimensionOf0(xt),sz00),
inference(rew,[status(thm),theory(equality)],[83,7]),
[iquote('0:Rew:83.0,7.0')] ).
cnf(87,plain,
( ~ aVector0(u)
| ~ aVector0(xt)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xt))
| equal(sdtasasdt0(u,xt),sz0z00) ),
inference(res,[status(thm),theory(equality)],[84,63]),
[iquote('0:Res:84.0,63.2')] ).
cnf(100,plain,
( ~ aVector0(u)
| ~ aVector0(xt)
| ~ equal(aDimensionOf0(u),sz00)
| equal(sdtasasdt0(u,xt),sz0z00) ),
inference(rew,[status(thm),theory(equality)],[84,87]),
[iquote('0:Rew:84.0,87.2')] ).
cnf(101,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),sz00)
| equal(sdtasasdt0(u,xt),sz0z00) ),
inference(mrr,[status(thm)],[100,4]),
[iquote('0:MRR:100.1,4.0')] ).
cnf(160,plain,
( ~ aVector0(xt)
| ~ aVector0(xt)
| ~ equal(aDimensionOf0(xt),sz00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(spr,[status(thm),theory(equality)],[101,23]),
[iquote('0:SpR:101.2,23.1')] ).
cnf(162,plain,
( ~ aVector0(xt)
| ~ equal(aDimensionOf0(xt),sz00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(obv,[status(thm),theory(equality)],[160]),
[iquote('0:Obv:160.0')] ).
cnf(163,plain,
( ~ aVector0(xt)
| ~ equal(sz00,sz00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(rew,[status(thm),theory(equality)],[84,162]),
[iquote('0:Rew:84.0,162.1')] ).
cnf(164,plain,
( ~ aVector0(xt)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(obv,[status(thm),theory(equality)],[163]),
[iquote('0:Obv:163.1')] ).
cnf(165,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(ssi,[status(thm)],[164,4]),
[iquote('0:SSi:164.0,4.0')] ).
cnf(501,plain,
( ~ aVector0(xs)
| ~ equal(aDimensionOf0(xs),sz00)
| ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(spl,[status(thm),theory(equality)],[101,50]),
[iquote('0:SpL:101.2,50.0')] ).
cnf(506,plain,
( ~ aVector0(xs)
| ~ equal(sz00,sz00)
| ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(rew,[status(thm),theory(equality)],[83,501]),
[iquote('0:Rew:83.0,501.1')] ).
cnf(507,plain,
( ~ aVector0(xs)
| ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(obv,[status(thm),theory(equality)],[506]),
[iquote('0:Obv:506.1')] ).
cnf(508,plain,
~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(ssi,[status(thm)],[507,3]),
[iquote('0:SSi:507.0,3.0')] ).
cnf(519,plain,
( ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(spl,[status(thm),theory(equality)],[20,508]),
[iquote('0:SpL:20.1,508.0')] ).
cnf(523,plain,
~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(ssi,[status(thm)],[519,2]),
[iquote('0:SSi:519.0,2.0')] ).
cnf(532,plain,
( ~ aVector0(xt)
| ~ equal(aDimensionOf0(xt),sz00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
inference(spl,[status(thm),theory(equality)],[101,523]),
[iquote('0:SpL:101.2,523.0')] ).
cnf(534,plain,
( ~ aVector0(xt)
| ~ equal(sz00,sz00)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
inference(rew,[status(thm),theory(equality)],[84,532]),
[iquote('0:Rew:84.0,532.1')] ).
cnf(535,plain,
( ~ aVector0(xt)
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)) ),
inference(obv,[status(thm),theory(equality)],[534]),
[iquote('0:Obv:534.1')] ).
cnf(536,plain,
~ sdtlseqdt0(sz0z00,sdtasdt0(sdtasasdt0(xs,xs),sz0z00)),
inference(ssi,[status(thm)],[535,4]),
[iquote('0:SSi:535.0,4.0')] ).
cnf(542,plain,
( ~ aScalar0(sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sz0z00) ),
inference(spl,[status(thm),theory(equality)],[19,536]),
[iquote('0:SpL:19.1,536.0')] ).
cnf(544,plain,
~ aScalar0(sdtasasdt0(xs,xs)),
inference(mrr,[status(thm)],[542,165]),
[iquote('0:MRR:542.1,165.0')] ).
cnf(548,plain,
( ~ aVector0(xs)
| ~ aVector0(xs)
| ~ equal(aDimensionOf0(xs),aDimensionOf0(xs)) ),
inference(sor,[status(thm)],[544,51]),
[iquote('0:SoR:544.0,51.3')] ).
cnf(551,plain,
~ aVector0(xs),
inference(obv,[status(thm),theory(equality)],[548]),
[iquote('0:Obv:548.2')] ).
cnf(552,plain,
$false,
inference(ssi,[status(thm)],[551,3]),
[iquote('0:SSi:551.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon May 30 21:24:12 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.50
% 0.20/0.50 SPASS V 3.9
% 0.20/0.50 SPASS beiseite: Proof found.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.50 SPASS derived 237 clauses, backtracked 0 clauses, performed 0 splits and kept 120 clauses.
% 0.20/0.50 SPASS allocated 98161 KBytes.
% 0.20/0.50 SPASS spent 0:00:00.14 on the problem.
% 0.20/0.50 0:00:00.04 for the input.
% 0.20/0.50 0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.50 0:00:00.00 for inferences.
% 0.20/0.50 0:00:00.00 for the backtracking.
% 0.20/0.50 0:00:00.03 for the reduction.
% 0.20/0.50
% 0.20/0.50
% 0.20/0.50 Here is a proof with depth 6, length 36 :
% 0.20/0.50 % SZS output start Refutation
% See solution above
% 0.20/0.50 Formulae used in the proof : mSZeroSc m__1678 m__1678_01 mScZero mScSqPos m__ mScPr mDefSPZ
% 0.20/0.50
%------------------------------------------------------------------------------