TSTP Solution File: RNG120+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG120+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 0.38s 0.58s
% Output   : Refutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   30 (  13 unt;   0 nHn;  30 RR)
%            Number of literals    :   63 (   0 equ;  38 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    :   13 (  13 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    aElement0(sz10),
    file('RNG120+1.p',unknown),
    [] ).

cnf(3,axiom,
    aElement0(xa),
    file('RNG120+1.p',unknown),
    [] ).

cnf(4,axiom,
    aElement0(xb),
    file('RNG120+1.p',unknown),
    [] ).

cnf(5,axiom,
    aIdeal0(xI),
    file('RNG120+1.p',unknown),
    [] ).

cnf(8,axiom,
    aElement0(xq),
    file('RNG120+1.p',unknown),
    [] ).

cnf(11,axiom,
    aElementOf0(xu,xI),
    file('RNG120+1.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ aIdeal0(u)
    | aSet0(u) ),
    file('RNG120+1.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ aElement0(u)
    | aElement0(smndt0(u)) ),
    file('RNG120+1.p',unknown),
    [] ).

cnf(31,axiom,
    ( ~ aElement0(u)
    | aIdeal0(slsdtgt0(u)) ),
    file('RNG120+1.p',unknown),
    [] ).

cnf(32,axiom,
    ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    file('RNG120+1.p',unknown),
    [] ).

cnf(33,axiom,
    equal(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),xI),
    file('RNG120+1.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ aSet0(u)
    | ~ aElementOf0(v,u)
    | aElement0(v) ),
    file('RNG120+1.p',unknown),
    [] ).

cnf(55,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | aElement0(sdtasdt0(v,u)) ),
    file('RNG120+1.p',unknown),
    [] ).

cnf(56,axiom,
    ( ~ aElement0(u)
    | equal(sdtasdt0(smndt0(sz10),u),smndt0(u)) ),
    file('RNG120+1.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ aElement0(u)
    | ~ equal(v,slsdtgt0(u))
    | aSet0(v) ),
    file('RNG120+1.p',unknown),
    [] ).

cnf(71,axiom,
    ( ~ aSet0(u)
    | ~ aSet0(v)
    | ~ equal(w,sdtpldt1(v,u))
    | aSet0(w) ),
    file('RNG120+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( ~ aIdeal0(u)
    | ~ aElement0(v)
    | ~ aElementOf0(w,u)
    | aElementOf0(sdtasdt0(v,w),u) ),
    file('RNG120+1.p',unknown),
    [] ).

cnf(144,plain,
    ( ~ aSet0(xI)
    | aElement0(xu) ),
    inference(res,[status(thm),theory(equality)],[11,48]),
    [iquote('0:Res:11.0,48.1')] ).

cnf(152,plain,
    aElement0(xu),
    inference(ssi,[status(thm)],[144,28,5]),
    [iquote('0:SSi:144.0,28.0,5.1')] ).

cnf(181,plain,
    ( ~ aElement0(u)
    | aSet0(slsdtgt0(u)) ),
    inference(eqr,[status(thm),theory(equality)],[61]),
    [iquote('0:EqR:61.1')] ).

cnf(264,plain,
    ( ~ aSet0(u)
    | ~ aSet0(v)
    | aSet0(sdtpldt1(v,u)) ),
    inference(eqr,[status(thm),theory(equality)],[71]),
    [iquote('0:EqR:71.2')] ).

cnf(278,plain,
    ( ~ aSet0(slsdtgt0(xb))
    | ~ aSet0(slsdtgt0(xa))
    | aSet0(xI) ),
    inference(spr,[status(thm),theory(equality)],[33,264]),
    [iquote('0:SpR:33.0,264.2')] ).

cnf(279,plain,
    aSet0(xI),
    inference(ssi,[status(thm)],[278,31,3,181,4]),
    [iquote('0:SSi:278.1,278.0,31.0,3.1,181.0,3.1,31.0,4.1,181.0,4.1')] ).

cnf(284,plain,
    ( ~ aElement0(u)
    | ~ aIdeal0(v)
    | ~ aElement0(smndt0(sz10))
    | ~ aElementOf0(u,v)
    | aElementOf0(smndt0(u),v) ),
    inference(spr,[status(thm),theory(equality)],[56,77]),
    [iquote('0:SpR:56.1,77.3')] ).

cnf(294,plain,
    ( ~ aElement0(u)
    | ~ aIdeal0(v)
    | ~ aElementOf0(u,v)
    | aElementOf0(smndt0(u),v) ),
    inference(ssi,[status(thm)],[284,29,2]),
    [iquote('0:SSi:284.2,29.0,2.1')] ).

cnf(419,plain,
    ( ~ aElement0(sdtasdt0(xq,xu))
    | ~ aIdeal0(xI)
    | ~ aElementOf0(sdtasdt0(xq,xu),xI) ),
    inference(res,[status(thm),theory(equality)],[294,32]),
    [iquote('0:Res:294.3,32.0')] ).

cnf(424,plain,
    ~ aElementOf0(sdtasdt0(xq,xu),xI),
    inference(ssi,[status(thm)],[419,5,279,55,8,152]),
    [iquote('0:SSi:419.1,419.0,5.0,279.0,55.2,8.0,152.0')] ).

cnf(435,plain,
    ( ~ aIdeal0(xI)
    | ~ aElement0(xq)
    | ~ aElementOf0(xu,xI) ),
    inference(res,[status(thm),theory(equality)],[77,424]),
    [iquote('0:Res:77.3,424.0')] ).

cnf(436,plain,
    ~ aElementOf0(xu,xI),
    inference(ssi,[status(thm)],[435,8,5,279]),
    [iquote('0:SSi:435.1,435.0,8.0,5.0,279.0')] ).

cnf(437,plain,
    $false,
    inference(mrr,[status(thm)],[436,11]),
    [iquote('0:MRR:436.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : RNG120+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon May 30 12:56:10 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.38/0.58  
% 0.38/0.58  SPASS V 3.9 
% 0.38/0.58  SPASS beiseite: Proof found.
% 0.38/0.58  % SZS status Theorem
% 0.38/0.58  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.38/0.58  SPASS derived 237 clauses, backtracked 0 clauses, performed 0 splits and kept 174 clauses.
% 0.38/0.58  SPASS allocated 99468 KBytes.
% 0.38/0.58  SPASS spent	0:00:00.22 on the problem.
% 0.38/0.58  		0:00:00.04 for the input.
% 0.38/0.58  		0:00:00.14 for the FLOTTER CNF translation.
% 0.38/0.58  		0:00:00.00 for inferences.
% 0.38/0.58  		0:00:00.00 for the backtracking.
% 0.38/0.58  		0:00:00.02 for the reduction.
% 0.38/0.58  
% 0.38/0.58  
% 0.38/0.58  Here is a proof with depth 3, length 30 :
% 0.38/0.58  % SZS output start Refutation
% See solution above
% 0.38/0.58  Formulae used in the proof : mSortsC_01 m__2091 m__2174 m__2666 m__2273 mDefIdeal mSortsU mPrIdeal m__ mEOfElem mSortsB_02 mMulMnOne mDefPrIdeal mDefSSum
% 0.38/0.58  
%------------------------------------------------------------------------------