TSTP Solution File: RNG052+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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  
%------------------------------------------------------------------------------