TSTP Solution File: RNG052+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG052+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 20:41:20 EDT 2022
% Result : Theorem 0.78s 0.96s
% Output : Refutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of clauses : 42 ( 17 unt; 11 nHn; 42 RR)
% Number of literals : 105 ( 0 equ; 57 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aVector0(xs),
file('RNG052+1.p',unknown),
[] ).
cnf(4,axiom,
aVector0(xt),
file('RNG052+1.p',unknown),
[] ).
cnf(5,axiom,
aVector0(xp),
file('RNG052+1.p',unknown),
[] ).
cnf(6,axiom,
aVector0(xq),
file('RNG052+1.p',unknown),
[] ).
cnf(21,axiom,
equal(sziznziztdt0(xs),xp),
file('RNG052+1.p',unknown),
[] ).
cnf(22,axiom,
equal(sziznziztdt0(xt),xq),
file('RNG052+1.p',unknown),
[] ).
cnf(23,axiom,
equal(aDimensionOf0(xt),aDimensionOf0(xs)),
file('RNG052+1.p',unknown),
[] ).
cnf(24,axiom,
~ equal(aDimensionOf0(xs),sz00),
file('RNG052+1.p',unknown),
[] ).
cnf(25,axiom,
equal(sdtasasdt0(xp,xp),xC),
file('RNG052+1.p',unknown),
[] ).
cnf(26,axiom,
equal(sdtasasdt0(xq,xq),xD),
file('RNG052+1.p',unknown),
[] ).
cnf(27,axiom,
equal(sdtasasdt0(xp,xq),xE),
file('RNG052+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ aVector0(u)
| aNaturalNumber0(aDimensionOf0(u)) ),
file('RNG052+1.p',unknown),
[] ).
cnf(41,axiom,
( ~ aNaturalNumber0(u)
| iLess0(u,szszuzczcdt0(u)) ),
file('RNG052+1.p',unknown),
[] ).
cnf(43,axiom,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('RNG052+1.p',unknown),
[] ).
cnf(68,axiom,
( ~ aVector0(u)
| ~ equal(v,sziznziztdt0(u))
| equal(aDimensionOf0(u),sz00)
| equal(szszuzczcdt0(aDimensionOf0(v)),aDimensionOf0(u)) ),
file('RNG052+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ aVector0(u)
| ~ aVector0(v)
| ~ equal(aDimensionOf0(v),aDimensionOf0(u))
| equal(aDimensionOf0(u),sz00)
| equal(aDimensionOf0(sziznziztdt0(v)),aDimensionOf0(sziznziztdt0(u))) ),
file('RNG052+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ aVector0(u)
| ~ aVector0(v)
| ~ equal(aDimensionOf0(v),aDimensionOf0(u))
| ~ iLess0(aDimensionOf0(v),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(v,u),sdtasasdt0(v,u)),sdtasdt0(sdtasasdt0(v,v),sdtasasdt0(u,u))) ),
file('RNG052+1.p',unknown),
[] ).
cnf(581,plain,
( ~ aVector0(xt)
| ~ equal(u,xq)
| equal(aDimensionOf0(xt),sz00)
| equal(szszuzczcdt0(aDimensionOf0(u)),aDimensionOf0(xt)) ),
inference(spl,[status(thm),theory(equality)],[22,68]),
[iquote('0:SpL:22.0,68.1')] ).
cnf(583,plain,
( ~ aVector0(xt)
| ~ equal(u,xq)
| equal(aDimensionOf0(xs),sz00)
| equal(szszuzczcdt0(aDimensionOf0(u)),aDimensionOf0(xs)) ),
inference(rew,[status(thm),theory(equality)],[23,581]),
[iquote('0:Rew:23.0,581.3,23.0,581.2')] ).
cnf(584,plain,
( ~ equal(u,xq)
| equal(aDimensionOf0(xs),sz00)
| equal(szszuzczcdt0(aDimensionOf0(u)),aDimensionOf0(xs)) ),
inference(ssi,[status(thm)],[583,4]),
[iquote('0:SSi:583.0,4.0')] ).
cnf(585,plain,
( ~ equal(u,xq)
| equal(szszuzczcdt0(aDimensionOf0(u)),aDimensionOf0(xs)) ),
inference(mrr,[status(thm)],[584,24]),
[iquote('0:MRR:584.1,24.0')] ).
cnf(1292,plain,
( ~ aVector0(xt)
| ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xt))
| equal(aDimensionOf0(xt),sz00)
| equal(aDimensionOf0(sziznziztdt0(u)),aDimensionOf0(xq)) ),
inference(spr,[status(thm),theory(equality)],[22,78]),
[iquote('0:SpR:22.0,78.4')] ).
cnf(1293,plain,
( ~ aVector0(xs)
| ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(aDimensionOf0(sziznziztdt0(u)),aDimensionOf0(xp)) ),
inference(spr,[status(thm),theory(equality)],[21,78]),
[iquote('0:SpR:21.0,78.4')] ).
cnf(1294,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(aDimensionOf0(sziznziztdt0(u)),aDimensionOf0(xp)) ),
inference(ssi,[status(thm)],[1293,3]),
[iquote('0:SSi:1293.0,3.0')] ).
cnf(1295,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(sziznziztdt0(u)),aDimensionOf0(xp)) ),
inference(mrr,[status(thm)],[1294,24]),
[iquote('0:MRR:1294.2,24.0')] ).
cnf(1296,plain,
( ~ aVector0(xt)
| ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(aDimensionOf0(sziznziztdt0(u)),aDimensionOf0(xq)) ),
inference(rew,[status(thm),theory(equality)],[23,1292]),
[iquote('0:Rew:23.0,1292.3,23.0,1292.2')] ).
cnf(1297,plain,
( ~ aVector0(xt)
| ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(aDimensionOf0(xq),aDimensionOf0(xp)) ),
inference(rew,[status(thm),theory(equality)],[1295,1296]),
[iquote('0:Rew:1295.2,1296.4')] ).
cnf(1298,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xs),sz00)
| equal(aDimensionOf0(xq),aDimensionOf0(xp)) ),
inference(ssi,[status(thm)],[1297,4]),
[iquote('0:SSi:1297.0,4.0')] ).
cnf(1299,plain,
( ~ aVector0(u)
| ~ equal(aDimensionOf0(u),aDimensionOf0(xs))
| equal(aDimensionOf0(xq),aDimensionOf0(xp)) ),
inference(mrr,[status(thm)],[1298,24]),
[iquote('0:MRR:1298.2,24.0')] ).
cnf(1756,plain,
( ~ aVector0(xq)
| ~ aVector0(xp)
| ~ equal(aDimensionOf0(xq),aDimensionOf0(xp))
| ~ iLess0(aDimensionOf0(xp),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))) ),
inference(spr,[status(thm),theory(equality)],[27,82]),
[iquote('0:SpR:27.0,82.4')] ).
cnf(1770,plain,
( ~ aVector0(xq)
| ~ aVector0(xp)
| ~ equal(aDimensionOf0(xq),aDimensionOf0(xp))
| ~ iLess0(aDimensionOf0(xp),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(rew,[status(thm),theory(equality)],[25,1756,26]),
[iquote('0:Rew:25.0,1756.4,26.0,1756.4')] ).
cnf(1771,plain,
( ~ equal(aDimensionOf0(xq),aDimensionOf0(xp))
| ~ iLess0(aDimensionOf0(xp),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)) ),
inference(ssi,[status(thm)],[1770,5,6]),
[iquote('0:SSi:1770.1,1770.0,5.0,6.0')] ).
cnf(1772,plain,
( ~ equal(aDimensionOf0(xq),aDimensionOf0(xp))
| ~ iLess0(aDimensionOf0(xp),aDimensionOf0(xs)) ),
inference(mrr,[status(thm)],[1771,43]),
[iquote('0:MRR:1771.2,43.0')] ).
cnf(2877,plain,
( ~ aVector0(xs)
| equal(aDimensionOf0(xq),aDimensionOf0(xp)) ),
inference(eqr,[status(thm),theory(equality)],[1299]),
[iquote('0:EqR:1299.1')] ).
cnf(2885,plain,
equal(aDimensionOf0(xq),aDimensionOf0(xp)),
inference(ssi,[status(thm)],[2877,3]),
[iquote('0:SSi:2877.0,3.0')] ).
cnf(2888,plain,
( ~ equal(aDimensionOf0(xp),aDimensionOf0(xp))
| ~ iLess0(aDimensionOf0(xp),aDimensionOf0(xs)) ),
inference(rew,[status(thm),theory(equality)],[2885,1772]),
[iquote('0:Rew:2885.0,1772.0')] ).
cnf(2892,plain,
~ iLess0(aDimensionOf0(xp),aDimensionOf0(xs)),
inference(obv,[status(thm),theory(equality)],[2888]),
[iquote('0:Obv:2888.0')] ).
cnf(2898,plain,
( ~ equal(xq,xq)
| equal(szszuzczcdt0(aDimensionOf0(xp)),aDimensionOf0(xs)) ),
inference(spr,[status(thm),theory(equality)],[2885,585]),
[iquote('0:SpR:2885.0,585.1')] ).
cnf(2915,plain,
equal(szszuzczcdt0(aDimensionOf0(xp)),aDimensionOf0(xs)),
inference(obv,[status(thm),theory(equality)],[2898]),
[iquote('0:Obv:2898.0')] ).
cnf(2934,plain,
( ~ aNaturalNumber0(aDimensionOf0(xp))
| iLess0(aDimensionOf0(xp),aDimensionOf0(xs)) ),
inference(spr,[status(thm),theory(equality)],[2915,41]),
[iquote('0:SpR:2915.0,41.1')] ).
cnf(2950,plain,
iLess0(aDimensionOf0(xp),aDimensionOf0(xs)),
inference(ssi,[status(thm)],[2934,38,5]),
[iquote('0:SSi:2934.0,38.0,5.1')] ).
cnf(2951,plain,
$false,
inference(mrr,[status(thm)],[2950,2892]),
[iquote('0:MRR:2950.0,2892.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG052+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 07:00:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.78/0.96
% 0.78/0.96 SPASS V 3.9
% 0.78/0.96 SPASS beiseite: Proof found.
% 0.78/0.96 % SZS status Theorem
% 0.78/0.96 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/0.96 SPASS derived 1557 clauses, backtracked 0 clauses, performed 0 splits and kept 744 clauses.
% 0.78/0.96 SPASS allocated 101143 KBytes.
% 0.78/0.96 SPASS spent 0:00:00.60 on the problem.
% 0.78/0.96 0:00:00.04 for the input.
% 0.78/0.96 0:00:00.03 for the FLOTTER CNF translation.
% 0.78/0.96 0:00:00.02 for inferences.
% 0.78/0.96 0:00:00.00 for the backtracking.
% 0.78/0.96 0:00:00.47 for the reduction.
% 0.78/0.96
% 0.78/0.96
% 0.78/0.96 Here is a proof with depth 4, length 42 :
% 0.78/0.96 % SZS output start Refutation
% See solution above
% 0.78/0.96 Formulae used in the proof : m__1678 m__1709 m__1726 m__1678_01 m__1692 m__1783 m__1800 m__1820 mDimNat mIH m__ mDefInit mZeroNat mEqInit m__1652
% 0.78/0.96
%------------------------------------------------------------------------------