TSTP Solution File: RNG049+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG049+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 20:41:19 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 21 ( 10 unt; 2 nHn; 21 RR)
% Number of literals : 48 ( 0 equ; 30 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aVector0(xs),
file('RNG049+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(aDimensionOf0(xs),sz00),
file('RNG049+1.p',unknown),
[] ).
cnf(7,axiom,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('RNG049+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ aVector0(u)
| aNaturalNumber0(aDimensionOf0(u)) ),
file('RNG049+1.p',unknown),
[] ).
cnf(14,axiom,
sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
file('RNG049+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| aScalar0(sdtasdt0(v,u)) ),
file('RNG049+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ aNaturalNumber0(u)
| ~ aVector0(v)
| aScalar0(sdtlbdtrb0(v,u)) ),
file('RNG049+1.p',unknown),
[] ).
cnf(28,axiom,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
file('RNG049+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ aVector0(u)
| ~ equal(v,sziznziztdt0(u))
| aVector0(v)
| equal(aDimensionOf0(u),sz00) ),
file('RNG049+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aVector0(u)
| ~ aVector0(v)
| ~ equal(aDimensionOf0(v),aDimensionOf0(u))
| aScalar0(sdtasasdt0(v,u)) ),
file('RNG049+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ aScalar0(u)
| ~ aScalar0(v)
| ~ sdtlseqdt0(sz0z00,v)
| ~ sdtlseqdt0(sz0z00,u)
| sdtlseqdt0(sz0z00,sdtpldt0(v,u)) ),
file('RNG049+1.p',unknown),
[] ).
cnf(43,axiom,
equal(sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtasasdt0(xs,xs)),
file('RNG049+1.p',unknown),
[] ).
cnf(151,plain,
( ~ aVector0(u)
| aVector0(sziznziztdt0(u))
| equal(aDimensionOf0(u),sz00) ),
inference(eqr,[status(thm),theory(equality)],[32]),
[iquote('0:EqR:32.1')] ).
cnf(974,plain,
( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(spr,[status(thm),theory(equality)],[43,41]),
[iquote('0:SpR:43.0,41.4')] ).
cnf(985,plain,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(ssi,[status(thm)],[974,25,26,3,11]),
[iquote('0:SSi:974.0,25.0,26.1,3.0,11.2,3.0,26.1,3.0,11.2,3.2')] ).
cnf(986,plain,
~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))),
inference(mrr,[status(thm)],[985,14,28,7]),
[iquote('0:MRR:985.1,985.2,985.3,14.0,28.0,7.0')] ).
cnf(987,plain,
( ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xs))
| ~ equal(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(sziznziztdt0(xs))) ),
inference(sor,[status(thm)],[986,38]),
[iquote('0:SoR:986.0,38.3')] ).
cnf(988,plain,
~ aVector0(sziznziztdt0(xs)),
inference(obv,[status(thm),theory(equality)],[987]),
[iquote('0:Obv:987.2')] ).
cnf(989,plain,
( ~ aVector0(xs)
| equal(aDimensionOf0(xs),sz00) ),
inference(sor,[status(thm)],[988,151]),
[iquote('0:SoR:988.0,151.1')] ).
cnf(991,plain,
equal(aDimensionOf0(xs),sz00),
inference(ssi,[status(thm)],[989,3]),
[iquote('0:SSi:989.0,3.0')] ).
cnf(992,plain,
$false,
inference(mrr,[status(thm)],[991,6]),
[iquote('0:MRR:991.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG049+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % 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 15:25:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.51
% 0.18/0.51 SPASS V 3.9
% 0.18/0.51 SPASS beiseite: Proof found.
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.51 SPASS derived 469 clauses, backtracked 0 clauses, performed 0 splits and kept 141 clauses.
% 0.18/0.51 SPASS allocated 98505 KBytes.
% 0.18/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.18/0.51 0:00:00.04 for the input.
% 0.18/0.51 0:00:00.04 for the FLOTTER CNF translation.
% 0.18/0.51 0:00:00.01 for inferences.
% 0.18/0.51 0:00:00.00 for the backtracking.
% 0.18/0.51 0:00:00.05 for the reduction.
% 0.18/0.51
% 0.18/0.51
% 0.18/0.51 Here is a proof with depth 3, length 21 :
% 0.18/0.51 % SZS output start Refutation
% See solution above
% 0.18/0.51 Formulae used in the proof : m__1542 m__1542_01 m__ mDimNat m__1590 mMulSc mElmSc mDefInit mZeroNat mScPr mPosMon m__1568
% 0.18/0.51
%------------------------------------------------------------------------------