TSTP Solution File: RNG071+2 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG071+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 20:41:23 EDT 2022

% Result   : Theorem 0.47s 0.67s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   28
% Syntax   : Number of clauses     :   71 (  30 unt;   5 nHn;  71 RR)
%            Number of literals    :  173 (   0 equ; 111 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  16 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    aScalar0(sz0z00),
    file('RNG071+2.p',unknown),
    [] ).

cnf(5,axiom,
    aVector0(xp),
    file('RNG071+2.p',unknown),
    [] ).

cnf(6,axiom,
    aVector0(xq),
    file('RNG071+2.p',unknown),
    [] ).

cnf(7,axiom,
    aScalar0(xA),
    file('RNG071+2.p',unknown),
    [] ).

cnf(8,axiom,
    aScalar0(xB),
    file('RNG071+2.p',unknown),
    [] ).

cnf(9,axiom,
    aScalar0(xC),
    file('RNG071+2.p',unknown),
    [] ).

cnf(10,axiom,
    aScalar0(xD),
    file('RNG071+2.p',unknown),
    [] ).

cnf(12,axiom,
    aScalar0(xF),
    file('RNG071+2.p',unknown),
    [] ).

cnf(13,axiom,
    aScalar0(xG),
    file('RNG071+2.p',unknown),
    [] ).

cnf(15,axiom,
    aScalar0(xR),
    file('RNG071+2.p',unknown),
    [] ).

cnf(16,axiom,
    aScalar0(xP),
    file('RNG071+2.p',unknown),
    [] ).

cnf(17,axiom,
    aScalar0(xS),
    file('RNG071+2.p',unknown),
    [] ).

cnf(25,axiom,
    equal(sdtasasdt0(xp,xp),xC),
    file('RNG071+2.p',unknown),
    [] ).

cnf(26,axiom,
    equal(sdtasasdt0(xq,xq),xD),
    file('RNG071+2.p',unknown),
    [] ).

cnf(28,axiom,
    equal(sdtasdt0(xA,xA),xF),
    file('RNG071+2.p',unknown),
    [] ).

cnf(29,axiom,
    equal(sdtasdt0(xB,xB),xG),
    file('RNG071+2.p',unknown),
    [] ).

cnf(31,axiom,
    equal(sdtasdt0(xC,xG),xR),
    file('RNG071+2.p',unknown),
    [] ).

cnf(33,axiom,
    equal(sdtasdt0(xF,xD),xS),
    file('RNG071+2.p',unknown),
    [] ).

cnf(54,axiom,
    ( ~ aScalar0(u)
    | sdtlseqdt0(sz0z00,sdtasdt0(u,u)) ),
    file('RNG071+2.p',unknown),
    [] ).

cnf(55,axiom,
    ( ~ aVector0(u)
    | sdtlseqdt0(sz0z00,sdtasasdt0(u,u)) ),
    file('RNG071+2.p',unknown),
    [] ).

cnf(56,axiom,
    ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
    file('RNG071+2.p',unknown),
    [] ).

cnf(65,axiom,
    ( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
    file('RNG071+2.p',unknown),
    [] ).

cnf(66,axiom,
    ( ~ aScalar0(u)
    | ~ aScalar0(v)
    | sdtlseqdt0(u,v)
    | sdtlseqdt0(v,u) ),
    file('RNG071+2.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ aScalar0(u)
    | ~ aScalar0(v)
    | ~ sdtlseqdt0(v,u)
    | ~ sdtlseqdt0(u,v)
    | equal(v,u) ),
    file('RNG071+2.p',unknown),
    [] ).

cnf(79,axiom,
    ( ~ aScalar0(u)
    | ~ aScalar0(v)
    | ~ sdtlseqdt0(sz0z00,v)
    | ~ sdtlseqdt0(sz0z00,u)
    | sdtlseqdt0(sz0z00,sdtpldt0(v,u)) ),
    file('RNG071+2.p',unknown),
    [] ).

cnf(80,axiom,
    ( ~ aScalar0(u)
    | ~ aScalar0(v)
    | ~ sdtlseqdt0(sz0z00,v)
    | ~ sdtlseqdt0(sz0z00,u)
    | sdtlseqdt0(sz0z00,sdtasdt0(v,u)) ),
    file('RNG071+2.p',unknown),
    [] ).

cnf(81,axiom,
    ( ~ aScalar0(u)
    | ~ aScalar0(v)
    | ~ aScalar0(w)
    | ~ sdtlseqdt0(v,u)
    | ~ sdtlseqdt0(w,v)
    | sdtlseqdt0(w,u) ),
    file('RNG071+2.p',unknown),
    [] ).

cnf(90,axiom,
    ( ~ aScalar0(u)
    | ~ aScalar0(v)
    | ~ aScalar0(w)
    | ~ aScalar0(x)
    | ~ sdtlseqdt0(x,w)
    | ~ sdtlseqdt0(v,u)
    | sdtlseqdt0(sdtpldt0(x,v),sdtpldt0(w,u)) ),
    file('RNG071+2.p',unknown),
    [] ).

cnf(151,plain,
    ( ~ aVector0(xq)
    | sdtlseqdt0(sz0z00,xD) ),
    inference(spr,[status(thm),theory(equality)],[26,55]),
    [iquote('0:SpR:26.0,55.1')] ).

cnf(152,plain,
    ( ~ aVector0(xp)
    | sdtlseqdt0(sz0z00,xC) ),
    inference(spr,[status(thm),theory(equality)],[25,55]),
    [iquote('0:SpR:25.0,55.1')] ).

cnf(153,plain,
    sdtlseqdt0(sz0z00,xD),
    inference(ssi,[status(thm)],[151,6]),
    [iquote('0:SSi:151.0,6.0')] ).

cnf(154,plain,
    sdtlseqdt0(sz0z00,xC),
    inference(ssi,[status(thm)],[152,5]),
    [iquote('0:SSi:152.0,5.0')] ).

cnf(155,plain,
    ( ~ aScalar0(xB)
    | sdtlseqdt0(sz0z00,xG) ),
    inference(spr,[status(thm),theory(equality)],[29,54]),
    [iquote('0:SpR:29.0,54.1')] ).

cnf(156,plain,
    ( ~ aScalar0(xA)
    | sdtlseqdt0(sz0z00,xF) ),
    inference(spr,[status(thm),theory(equality)],[28,54]),
    [iquote('0:SpR:28.0,54.1')] ).

cnf(159,plain,
    sdtlseqdt0(sz0z00,xG),
    inference(ssi,[status(thm)],[155,8]),
    [iquote('0:SSi:155.0,8.0')] ).

cnf(160,plain,
    sdtlseqdt0(sz0z00,xF),
    inference(ssi,[status(thm)],[156,7]),
    [iquote('0:SSi:156.0,7.0')] ).

cnf(573,plain,
    ( ~ aScalar0(xD)
    | ~ aScalar0(xF)
    | ~ sdtlseqdt0(sz0z00,xF)
    | ~ sdtlseqdt0(sz0z00,xD)
    | sdtlseqdt0(sz0z00,xS) ),
    inference(spr,[status(thm),theory(equality)],[33,80]),
    [iquote('0:SpR:33.0,80.4')] ).

cnf(575,plain,
    ( ~ aScalar0(xG)
    | ~ aScalar0(xC)
    | ~ sdtlseqdt0(sz0z00,xC)
    | ~ sdtlseqdt0(sz0z00,xG)
    | sdtlseqdt0(sz0z00,xR) ),
    inference(spr,[status(thm),theory(equality)],[31,80]),
    [iquote('0:SpR:31.0,80.4')] ).

cnf(589,plain,
    ( ~ sdtlseqdt0(sz0z00,xF)
    | ~ sdtlseqdt0(sz0z00,xD)
    | sdtlseqdt0(sz0z00,xS) ),
    inference(ssi,[status(thm)],[573,12,10]),
    [iquote('0:SSi:573.1,573.0,12.0,10.0')] ).

cnf(590,plain,
    sdtlseqdt0(sz0z00,xS),
    inference(mrr,[status(thm)],[589,160,153]),
    [iquote('0:MRR:589.0,589.1,160.0,153.0')] ).

cnf(593,plain,
    ( ~ sdtlseqdt0(sz0z00,xC)
    | ~ sdtlseqdt0(sz0z00,xG)
    | sdtlseqdt0(sz0z00,xR) ),
    inference(ssi,[status(thm)],[575,9,13]),
    [iquote('0:SSi:575.1,575.0,9.0,13.0')] ).

cnf(594,plain,
    sdtlseqdt0(sz0z00,xR),
    inference(mrr,[status(thm)],[593,154,159]),
    [iquote('0:MRR:593.0,593.1,154.0,159.0')] ).

cnf(621,plain,
    ( ~ aScalar0(xP)
    | ~ aScalar0(xP)
    | ~ sdtlseqdt0(sz0z00,xP)
    | ~ sdtlseqdt0(sz0z00,xP)
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
    inference(res,[status(thm),theory(equality)],[79,65]),
    [iquote('0:Res:79.4,65.0')] ).

cnf(623,plain,
    ( ~ aScalar0(xP)
    | ~ sdtlseqdt0(sz0z00,xP)
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
    inference(obv,[status(thm),theory(equality)],[621]),
    [iquote('0:Obv:621.2')] ).

cnf(624,plain,
    ( ~ sdtlseqdt0(sz0z00,xP)
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
    inference(ssi,[status(thm)],[623,16]),
    [iquote('0:SSi:623.0,16.0')] ).

cnf(687,plain,
    ( ~ aScalar0(xS)
    | ~ aScalar0(xR)
    | ~ sdtlseqdt0(sz0z00,xR)
    | ~ sdtlseqdt0(sz0z00,xS)
    | ~ sdtlseqdt0(sz0z00,xP) ),
    inference(res,[status(thm),theory(equality)],[79,624]),
    [iquote('0:Res:79.4,624.1')] ).

cnf(688,plain,
    ( ~ sdtlseqdt0(sz0z00,xR)
    | ~ sdtlseqdt0(sz0z00,xS)
    | ~ sdtlseqdt0(sz0z00,xP) ),
    inference(ssi,[status(thm)],[687,15,17]),
    [iquote('0:SSi:687.1,687.0,15.0,17.0')] ).

cnf(689,plain,
    ~ sdtlseqdt0(sz0z00,xP),
    inference(mrr,[status(thm)],[688,594,590]),
    [iquote('0:MRR:688.0,688.1,594.0,590.0')] ).

cnf(864,plain,
    ( ~ aScalar0(xS)
    | ~ aScalar0(sz0z00)
    | ~ aScalar0(u)
    | ~ sdtlseqdt0(u,sz0z00)
    | sdtlseqdt0(u,xS) ),
    inference(res,[status(thm),theory(equality)],[590,81]),
    [iquote('0:Res:590.0,81.3')] ).

cnf(865,plain,
    ( ~ aScalar0(xR)
    | ~ aScalar0(sz0z00)
    | ~ aScalar0(u)
    | ~ sdtlseqdt0(u,sz0z00)
    | sdtlseqdt0(u,xR) ),
    inference(res,[status(thm),theory(equality)],[594,81]),
    [iquote('0:Res:594.0,81.3')] ).

cnf(872,plain,
    ( ~ aScalar0(u)
    | ~ sdtlseqdt0(u,sz0z00)
    | sdtlseqdt0(u,xS) ),
    inference(ssi,[status(thm)],[864,2,17]),
    [iquote('0:SSi:864.1,864.0,2.0,17.0')] ).

cnf(873,plain,
    ( ~ aScalar0(u)
    | ~ sdtlseqdt0(u,sz0z00)
    | sdtlseqdt0(u,xR) ),
    inference(ssi,[status(thm)],[865,2,15]),
    [iquote('0:SSi:865.1,865.0,2.0,15.0')] ).

cnf(1415,plain,
    ( ~ aScalar0(xS)
    | ~ aScalar0(xP)
    | ~ aScalar0(xR)
    | ~ aScalar0(xP)
    | ~ sdtlseqdt0(xP,xR)
    | ~ sdtlseqdt0(xP,xS) ),
    inference(res,[status(thm),theory(equality)],[90,56]),
    [iquote('0:Res:90.6,56.0')] ).

cnf(1418,plain,
    ( ~ aScalar0(xS)
    | ~ aScalar0(xR)
    | ~ aScalar0(xP)
    | ~ sdtlseqdt0(xP,xR)
    | ~ sdtlseqdt0(xP,xS) ),
    inference(obv,[status(thm),theory(equality)],[1415]),
    [iquote('0:Obv:1415.1')] ).

cnf(1419,plain,
    ( ~ sdtlseqdt0(xP,xR)
    | ~ sdtlseqdt0(xP,xS) ),
    inference(ssi,[status(thm)],[1418,16,15,17]),
    [iquote('0:SSi:1418.2,1418.1,1418.0,16.0,15.0,17.0')] ).

cnf(1463,plain,
    ( ~ aScalar0(xP)
    | ~ sdtlseqdt0(xP,sz0z00)
    | ~ sdtlseqdt0(xP,xR) ),
    inference(res,[status(thm),theory(equality)],[872,1419]),
    [iquote('0:Res:872.2,1419.1')] ).

cnf(1464,plain,
    ( ~ sdtlseqdt0(xP,sz0z00)
    | ~ sdtlseqdt0(xP,xR) ),
    inference(ssi,[status(thm)],[1463,16]),
    [iquote('0:SSi:1463.0,16.0')] ).

cnf(1597,plain,
    ( ~ aScalar0(xP)
    | ~ aScalar0(xR)
    | ~ sdtlseqdt0(xP,sz0z00)
    | sdtlseqdt0(xR,xP) ),
    inference(res,[status(thm),theory(equality)],[66,1464]),
    [iquote('0:Res:66.2,1464.1')] ).

cnf(1599,plain,
    ( ~ sdtlseqdt0(xP,sz0z00)
    | sdtlseqdt0(xR,xP) ),
    inference(ssi,[status(thm)],[1597,15,16]),
    [iquote('0:SSi:1597.1,1597.0,15.0,16.0')] ).

cnf(1600,plain,
    ( ~ aScalar0(xP)
    | ~ aScalar0(sz0z00)
    | sdtlseqdt0(sz0z00,xP)
    | sdtlseqdt0(xR,xP) ),
    inference(res,[status(thm),theory(equality)],[66,1599]),
    [iquote('0:Res:66.2,1599.0')] ).

cnf(1602,plain,
    ( sdtlseqdt0(sz0z00,xP)
    | sdtlseqdt0(xR,xP) ),
    inference(ssi,[status(thm)],[1600,2,16]),
    [iquote('0:SSi:1600.1,1600.0,2.0,16.0')] ).

cnf(1603,plain,
    sdtlseqdt0(xR,xP),
    inference(mrr,[status(thm)],[1602,689]),
    [iquote('0:MRR:1602.0,689.0')] ).

cnf(1605,plain,
    ( ~ aScalar0(xP)
    | ~ aScalar0(xR)
    | ~ sdtlseqdt0(xP,xR)
    | equal(xP,xR) ),
    inference(res,[status(thm),theory(equality)],[1603,77]),
    [iquote('0:Res:1603.0,77.2')] ).

cnf(1606,plain,
    ( ~ sdtlseqdt0(xP,xR)
    | equal(xP,xR) ),
    inference(ssi,[status(thm)],[1605,15,16]),
    [iquote('0:SSi:1605.1,1605.0,15.0,16.0')] ).

cnf(1720,plain,
    ( ~ aScalar0(xP)
    | ~ sdtlseqdt0(xP,sz0z00)
    | equal(xP,xR) ),
    inference(res,[status(thm),theory(equality)],[873,1606]),
    [iquote('0:Res:873.2,1606.0')] ).

cnf(1721,plain,
    ( ~ sdtlseqdt0(xP,sz0z00)
    | equal(xP,xR) ),
    inference(ssi,[status(thm)],[1720,16]),
    [iquote('0:SSi:1720.0,16.0')] ).

cnf(1727,plain,
    ( ~ aScalar0(xP)
    | ~ aScalar0(sz0z00)
    | sdtlseqdt0(sz0z00,xP)
    | equal(xP,xR) ),
    inference(res,[status(thm),theory(equality)],[66,1721]),
    [iquote('0:Res:66.2,1721.0')] ).

cnf(1729,plain,
    ( sdtlseqdt0(sz0z00,xP)
    | equal(xP,xR) ),
    inference(ssi,[status(thm)],[1727,2,16]),
    [iquote('0:SSi:1727.1,1727.0,2.0,16.0')] ).

cnf(1730,plain,
    equal(xP,xR),
    inference(mrr,[status(thm)],[1729,689]),
    [iquote('0:MRR:1729.0,689.0')] ).

cnf(1740,plain,
    ~ sdtlseqdt0(sz0z00,xR),
    inference(rew,[status(thm),theory(equality)],[1730,689]),
    [iquote('0:Rew:1730.0,689.0')] ).

cnf(1766,plain,
    $false,
    inference(mrr,[status(thm)],[1740,594]),
    [iquote('0:MRR:1740.0,594.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG071+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon May 30 10:30:59 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.47/0.67  
% 0.47/0.67  SPASS V 3.9 
% 0.47/0.67  SPASS beiseite: Proof found.
% 0.47/0.67  % SZS status Theorem
% 0.47/0.67  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.47/0.67  SPASS derived 914 clauses, backtracked 0 clauses, performed 0 splits and kept 507 clauses.
% 0.47/0.67  SPASS allocated 99540 KBytes.
% 0.47/0.67  SPASS spent	0:00:00.31 on the problem.
% 0.47/0.67  		0:00:00.04 for the input.
% 0.47/0.67  		0:00:00.04 for the FLOTTER CNF translation.
% 0.47/0.67  		0:00:00.01 for inferences.
% 0.47/0.67  		0:00:00.00 for the backtracking.
% 0.47/0.67  		0:00:00.20 for the reduction.
% 0.47/0.67  
% 0.47/0.67  
% 0.47/0.67  Here is a proof with depth 8, length 71 :
% 0.47/0.67  % SZS output start Refutation
% See solution above
% 0.47/0.67  Formulae used in the proof : mSZeroSc m__1709 m__1726 m__1746 m__1766 m__1783 m__1800 m__1837 m__1854 m__1892 m__1911 m__1930 mSqPos mScSqPos m__2590 m__ mLETot mLEASm mPosMon mLETrn mLEMon
% 0.47/0.67  
%------------------------------------------------------------------------------