TSTP Solution File: RNG122+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG122+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 20:41:32 EDT 2022

% Result   : Theorem 0.92s 1.11s
% Output   : Refutation 0.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   16
% Syntax   : Number of clauses     :   34 (  16 unt;   0 nHn;  34 RR)
%            Number of literals    :   65 (   0 equ;  39 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    aElement0(xb),
    file('RNG122+1.p',unknown),
    [] ).

cnf(5,axiom,
    aIdeal0(xI),
    file('RNG122+1.p',unknown),
    [] ).

cnf(8,axiom,
    aElement0(xq),
    file('RNG122+1.p',unknown),
    [] ).

cnf(9,axiom,
    aElement0(xr),
    file('RNG122+1.p',unknown),
    [] ).

cnf(11,axiom,
    aElementOf0(xu,xI),
    file('RNG122+1.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ aIdeal0(u)
    | aSet0(u) ),
    file('RNG122+1.p',unknown),
    [] ).

cnf(30,axiom,
    ( ~ aElement0(u)
    | aElement0(smndt0(u)) ),
    file('RNG122+1.p',unknown),
    [] ).

cnf(36,axiom,
    equal(sdtpldt0(sdtasdt0(xq,xu),xr),xb),
    file('RNG122+1.p',unknown),
    [] ).

cnf(37,axiom,
    ( ~ aElement0(u)
    | equal(sdtpldt0(u,sz00),u) ),
    file('RNG122+1.p',unknown),
    [] ).

cnf(47,axiom,
    ~ equal(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),xr),
    file('RNG122+1.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ aElement0(u)
    | equal(sdtpldt0(u,smndt0(u)),sz00) ),
    file('RNG122+1.p',unknown),
    [] ).

cnf(50,axiom,
    ( ~ aSet0(u)
    | ~ aElementOf0(v,u)
    | aElement0(v) ),
    file('RNG122+1.p',unknown),
    [] ).

cnf(57,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | aElement0(sdtasdt0(v,u)) ),
    file('RNG122+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtpldt0(v,u),sdtpldt0(u,v)) ),
    file('RNG122+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | equal(sdtasdt0(v,u),sdtasdt0(u,v)) ),
    file('RNG122+1.p',unknown),
    [] ).

cnf(98,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aElement0(w)
    | equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u))) ),
    file('RNG122+1.p',unknown),
    [] ).

cnf(144,plain,
    ( ~ aSet0(xI)
    | aElement0(xu) ),
    inference(res,[status(thm),theory(equality)],[11,50]),
    [iquote('0:Res:11.0,50.1')] ).

cnf(153,plain,
    aElement0(xu),
    inference(ssi,[status(thm)],[144,29,5]),
    [iquote('0:SSi:144.0,29.0,5.1')] ).

cnf(191,plain,
    ( ~ aElement0(xu)
    | ~ aElement0(xq)
    | equal(sdtpldt0(sdtasdt0(xu,xq),xr),xb) ),
    inference(spr,[status(thm),theory(equality)],[69,36]),
    [iquote('0:SpR:69.2,36.0')] ).

cnf(213,plain,
    ( ~ aElement0(xu)
    | ~ aElement0(xq)
    | ~ equal(sdtpldt0(smndt0(sdtasdt0(xu,xq)),xb),xr) ),
    inference(spl,[status(thm),theory(equality)],[69,47]),
    [iquote('0:SpL:69.2,47.0')] ).

cnf(217,plain,
    equal(sdtpldt0(sdtasdt0(xu,xq),xr),xb),
    inference(ssi,[status(thm)],[191,8,153]),
    [iquote('0:SSi:191.1,191.0,8.0,153.0')] ).

cnf(226,plain,
    ~ equal(sdtpldt0(smndt0(sdtasdt0(xu,xq)),xb),xr),
    inference(ssi,[status(thm)],[213,8,153]),
    [iquote('0:SSi:213.1,213.0,8.0,153.0')] ).

cnf(237,plain,
    ( ~ aElement0(xr)
    | ~ aElement0(sdtasdt0(xu,xq))
    | equal(sdtpldt0(xr,sdtasdt0(xu,xq)),xb) ),
    inference(spr,[status(thm),theory(equality)],[68,217]),
    [iquote('0:SpR:68.2,217.0')] ).

cnf(259,plain,
    equal(sdtpldt0(xr,sdtasdt0(xu,xq)),xb),
    inference(ssi,[status(thm)],[237,57,153,8,9]),
    [iquote('0:SSi:237.1,237.0,57.0,153.0,8.0,9.2')] ).

cnf(271,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(smndt0(sdtasdt0(xu,xq)))
    | ~ equal(sdtpldt0(xb,smndt0(sdtasdt0(xu,xq))),xr) ),
    inference(spl,[status(thm),theory(equality)],[68,226]),
    [iquote('0:SpL:68.2,226.0')] ).

cnf(273,plain,
    ~ equal(sdtpldt0(xb,smndt0(sdtasdt0(xu,xq))),xr),
    inference(ssi,[status(thm)],[271,30,57,153,8,4]),
    [iquote('0:SSi:271.1,271.0,30.0,57.0,153.0,8.2,4.1')] ).

cnf(841,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sdtasdt0(xu,xq))
    | ~ aElement0(xr)
    | equal(sdtpldt0(xr,sdtpldt0(sdtasdt0(xu,xq),u)),sdtpldt0(xb,u)) ),
    inference(spr,[status(thm),theory(equality)],[259,98]),
    [iquote('0:SpR:259.0,98.3')] ).

cnf(853,plain,
    ( ~ aElement0(u)
    | equal(sdtpldt0(xr,sdtpldt0(sdtasdt0(xu,xq),u)),sdtpldt0(xb,u)) ),
    inference(ssi,[status(thm)],[841,9,57,153,8]),
    [iquote('0:SSi:841.2,841.1,9.0,57.0,153.2,8.0')] ).

cnf(2668,plain,
    ( ~ aElement0(sdtasdt0(xu,xq))
    | ~ aElement0(smndt0(sdtasdt0(xu,xq)))
    | equal(sdtpldt0(xb,smndt0(sdtasdt0(xu,xq))),sdtpldt0(xr,sz00)) ),
    inference(spr,[status(thm),theory(equality)],[48,853]),
    [iquote('0:SpR:48.1,853.1')] ).

cnf(2675,plain,
    equal(sdtpldt0(xb,smndt0(sdtasdt0(xu,xq))),sdtpldt0(xr,sz00)),
    inference(ssi,[status(thm)],[2668,30,57,153,8]),
    [iquote('0:SSi:2668.1,2668.0,30.0,57.0,153.2,8.0,57.0,153.2,8.1')] ).

cnf(2676,plain,
    ~ equal(sdtpldt0(xr,sz00),xr),
    inference(rew,[status(thm),theory(equality)],[2675,273]),
    [iquote('0:Rew:2675.0,273.0')] ).

cnf(2731,plain,
    ( ~ aElement0(xr)
    | ~ equal(xr,xr) ),
    inference(spl,[status(thm),theory(equality)],[37,2676]),
    [iquote('0:SpL:37.1,2676.0')] ).

cnf(2732,plain,
    ~ aElement0(xr),
    inference(obv,[status(thm),theory(equality)],[2731]),
    [iquote('0:Obv:2731.1')] ).

cnf(2733,plain,
    $false,
    inference(ssi,[status(thm)],[2732,9]),
    [iquote('0:SSi:2732.0,9.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : RNG122+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n021.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 21:49:44 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.92/1.11  
% 0.92/1.11  SPASS V 3.9 
% 0.92/1.11  SPASS beiseite: Proof found.
% 0.92/1.11  % SZS status Theorem
% 0.92/1.11  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.92/1.11  SPASS derived 1593 clauses, backtracked 0 clauses, performed 0 splits and kept 685 clauses.
% 0.92/1.11  SPASS allocated 100792 KBytes.
% 0.92/1.11  SPASS spent	0:00:00.73 on the problem.
% 0.92/1.11  		0:00:00.04 for the input.
% 0.92/1.11  		0:00:00.15 for the FLOTTER CNF translation.
% 0.92/1.11  		0:00:00.04 for inferences.
% 0.92/1.11  		0:00:00.00 for the backtracking.
% 0.92/1.11  		0:00:00.46 for the reduction.
% 0.92/1.11  
% 0.92/1.11  
% 0.92/1.11  Here is a proof with depth 4, length 34 :
% 0.92/1.11  % SZS output start Refutation
% See solution above
% 0.92/1.11  Formulae used in the proof : m__2091 m__2174 m__2666 m__2273 mDefIdeal mSortsU mAddZero m__ mAddInvr mEOfElem mSortsB_02 mAddComm mMulComm mAddAsso
% 0.92/1.11  
%------------------------------------------------------------------------------