TSTP Solution File: RNG108+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG108+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 20:41:30 EDT 2022

% Result   : Theorem 3.55s 3.77s
% Output   : Refutation 3.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   18
% Syntax   : Number of clauses     :   55 (  15 unt;   0 nHn;  55 RR)
%            Number of literals    :  153 (   0 equ; 110 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    aElement0(sz00),
    file('RNG108+1.p',unknown),
    [] ).

cnf(2,axiom,
    aElement0(sz10),
    file('RNG108+1.p',unknown),
    [] ).

cnf(3,axiom,
    aElement0(xa),
    file('RNG108+1.p',unknown),
    [] ).

cnf(4,axiom,
    aElement0(xb),
    file('RNG108+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(sz00,sz10),
    file('RNG108+1.p',unknown),
    [] ).

cnf(13,axiom,
    aGcdOfAnd0(xc,xa,xb),
    file('RNG108+1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ aIdeal0(u)
    | aSet0(u) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ aElement0(u)
    | aIdeal0(slsdtgt0(u)) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ aElement0(u)
    | equal(sdtasdt0(u,sz10),u) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ aElement0(u)
    | equal(sdtasdt0(u,sz00),sz00) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ aElement0(u)
    | equal(sdtasdt0(sz00,u),sz00) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(29,axiom,
    ( ~ aSet0(u)
    | ~ aElementOf0(v,u)
    | aElement0(v) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(33,axiom,
    ( ~ aElement0(u)
    | ~ aDivisorOf0(v,u)
    | aElement0(v) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(41,axiom,
    ( ~ aElement0(u)
    | ~ equal(v,slsdtgt0(u))
    | aSet0(v) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(53,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ aGcdOfAnd0(w,v,u)
    | aDivisorOf0(w,u) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(56,axiom,
    ( ~ aIdeal0(u)
    | ~ aElement0(v)
    | ~ aElementOf0(w,u)
    | aElementOf0(sdtasdt0(v,w),u) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ aElement0(u)
    | ~ aElement0(v)
    | ~ equal(w,slsdtgt0(u))
    | ~ equal(sdtasdt0(u,v),x)
    | aElementOf0(x,w) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( ~ aElementOf0(xb,slsdtgt0(xb))
    | ~ aElementOf0(xa,slsdtgt0(xa))
    | ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElementOf0(sz00,slsdtgt0(xa)) ),
    file('RNG108+1.p',unknown),
    [] ).

cnf(142,plain,
    ( ~ aElement0(u)
    | aSet0(slsdtgt0(u)) ),
    inference(eqr,[status(thm),theory(equality)],[41]),
    [iquote('0:EqR:41.1')] ).

cnf(205,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xa)
    | aDivisorOf0(xc,xb) ),
    inference(res,[status(thm),theory(equality)],[13,53]),
    [iquote('0:Res:13.0,53.2')] ).

cnf(206,plain,
    aDivisorOf0(xc,xb),
    inference(ssi,[status(thm)],[205,3,4]),
    [iquote('0:SSi:205.1,205.0,3.0,4.0')] ).

cnf(210,plain,
    ( ~ aElement0(xb)
    | aElement0(xc) ),
    inference(res,[status(thm),theory(equality)],[206,33]),
    [iquote('0:Res:206.0,33.1')] ).

cnf(211,plain,
    aElement0(xc),
    inference(ssi,[status(thm)],[210,4]),
    [iquote('0:SSi:210.0,4.0')] ).

cnf(216,plain,
    ( ~ aElement0(u)
    | ~ aIdeal0(v)
    | ~ aElement0(sz00)
    | ~ aElementOf0(u,v)
    | aElementOf0(sz00,v) ),
    inference(spr,[status(thm),theory(equality)],[24,56]),
    [iquote('0:SpR:24.1,56.3')] ).

cnf(224,plain,
    ( ~ aIdeal0(u)
    | ~ aElement0(v)
    | ~ aSet0(u)
    | ~ aElementOf0(w,u)
    | aElement0(sdtasdt0(v,w)) ),
    inference(res,[status(thm),theory(equality)],[56,29]),
    [iquote('0:Res:56.3,29.1')] ).

cnf(225,plain,
    ( ~ aElement0(u)
    | ~ aIdeal0(v)
    | ~ aElementOf0(u,v)
    | aElementOf0(sz00,v) ),
    inference(ssi,[status(thm)],[216,1]),
    [iquote('0:SSi:216.2,1.0')] ).

cnf(227,plain,
    ( ~ aIdeal0(u)
    | ~ aElement0(v)
    | ~ aElementOf0(w,u)
    | aElement0(sdtasdt0(v,w)) ),
    inference(ssi,[status(thm)],[224,14]),
    [iquote('0:SSi:224.2,14.1')] ).

cnf(234,plain,
    ( ~ aIdeal0(u)
    | ~ aElement0(v)
    | ~ aElement0(sdtasdt0(v,w))
    | ~ aIdeal0(u)
    | ~ aElementOf0(w,u)
    | aElementOf0(sz00,u) ),
    inference(res,[status(thm),theory(equality)],[56,225]),
    [iquote('0:Res:56.3,225.2')] ).

cnf(235,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sdtasdt0(u,v))
    | ~ aIdeal0(w)
    | ~ aElementOf0(v,w)
    | aElementOf0(sz00,w) ),
    inference(obv,[status(thm),theory(equality)],[234]),
    [iquote('0:Obv:234.0')] ).

cnf(236,plain,
    ( ~ aElement0(u)
    | ~ aIdeal0(v)
    | ~ aElementOf0(w,v)
    | aElementOf0(sz00,v) ),
    inference(mrr,[status(thm)],[235,227]),
    [iquote('0:MRR:235.1,227.3')] ).

cnf(237,plain,
    ( ~ aIdeal0(u)
    | ~ aElementOf0(v,u)
    | aElementOf0(sz00,u) ),
    inference(ems,[status(thm)],[236,211]),
    [iquote('0:EmS:236.0,211.0')] ).

cnf(3996,plain,
    ~ aElementOf0(xb,slsdtgt0(xb)),
    inference(spt,[spt(split,[position(s1)])],[76]),
    [iquote('1:Spt:76.0')] ).

cnf(4859,plain,
    ( ~ aElement0(u)
    | ~ aElement0(u)
    | ~ aElement0(sz10)
    | ~ equal(v,slsdtgt0(u))
    | ~ equal(u,w)
    | aElementOf0(w,v) ),
    inference(spl,[status(thm),theory(equality)],[21,68]),
    [iquote('0:SpL:21.1,68.3')] ).

cnf(4860,plain,
    ( ~ aElement0(u)
    | ~ aElement0(u)
    | ~ aElement0(sz00)
    | ~ equal(v,slsdtgt0(u))
    | ~ equal(sz00,w)
    | aElementOf0(w,v) ),
    inference(spl,[status(thm),theory(equality)],[23,68]),
    [iquote('0:SpL:23.1,68.3')] ).

cnf(4866,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sz00)
    | ~ equal(v,slsdtgt0(u))
    | ~ equal(sz00,w)
    | aElementOf0(w,v) ),
    inference(obv,[status(thm),theory(equality)],[4860]),
    [iquote('0:Obv:4860.0')] ).

cnf(4867,plain,
    ( ~ aElement0(u)
    | ~ equal(v,slsdtgt0(u))
    | ~ equal(sz00,w)
    | aElementOf0(w,v) ),
    inference(ssi,[status(thm)],[4866,1]),
    [iquote('0:SSi:4866.1,1.0')] ).

cnf(4868,plain,
    ( ~ aElement0(u)
    | ~ aElement0(sz10)
    | ~ equal(v,slsdtgt0(u))
    | ~ equal(u,w)
    | aElementOf0(w,v) ),
    inference(obv,[status(thm),theory(equality)],[4859]),
    [iquote('0:Obv:4859.0')] ).

cnf(4869,plain,
    ( ~ aElement0(u)
    | ~ equal(v,slsdtgt0(u))
    | ~ equal(u,w)
    | aElementOf0(w,v) ),
    inference(ssi,[status(thm)],[4868,2]),
    [iquote('0:SSi:4868.1,2.0')] ).

cnf(8261,plain,
    ( ~ aElement0(u)
    | ~ equal(sz00,v)
    | aElementOf0(v,slsdtgt0(u)) ),
    inference(eqr,[status(thm),theory(equality)],[4867]),
    [iquote('0:EqR:4867.1')] ).

cnf(8271,plain,
    ( ~ aElement0(u)
    | ~ aIdeal0(slsdtgt0(u))
    | ~ equal(sz00,v)
    | aElementOf0(sz00,slsdtgt0(u)) ),
    inference(res,[status(thm),theory(equality)],[8261,237]),
    [iquote('0:Res:8261.2,237.1')] ).

cnf(8312,plain,
    ( ~ aElement0(u)
    | ~ aIdeal0(slsdtgt0(u))
    | aElementOf0(sz00,slsdtgt0(u)) ),
    inference(aed,[status(thm),theory(equality)],[7,8271]),
    [iquote('0:AED:7.0,8271.2')] ).

cnf(8313,plain,
    ( ~ aElement0(u)
    | aElementOf0(sz00,slsdtgt0(u)) ),
    inference(ssi,[status(thm)],[8312,17,142]),
    [iquote('0:SSi:8312.1,17.1,142.1')] ).

cnf(9274,plain,
    ( ~ aElement0(u)
    | ~ equal(u,v)
    | aElementOf0(v,slsdtgt0(u)) ),
    inference(eqr,[status(thm),theory(equality)],[4869]),
    [iquote('0:EqR:4869.1')] ).

cnf(10296,plain,
    ( ~ aElement0(xb)
    | ~ equal(xb,xb) ),
    inference(res,[status(thm),theory(equality)],[9274,3996]),
    [iquote('1:Res:9274.2,3996.0')] ).

cnf(10302,plain,
    ~ aElement0(xb),
    inference(obv,[status(thm),theory(equality)],[10296]),
    [iquote('1:Obv:10296.1')] ).

cnf(10303,plain,
    $false,
    inference(ssi,[status(thm)],[10302,4]),
    [iquote('1:SSi:10302.0,4.0')] ).

cnf(10337,plain,
    aElementOf0(xb,slsdtgt0(xb)),
    inference(spt,[spt(split,[position(sa)])],[10303,3996]),
    [iquote('1:Spt:10303.0,76.0,3996.0')] ).

cnf(10338,plain,
    ( ~ aElementOf0(xa,slsdtgt0(xa))
    | ~ aElementOf0(sz00,slsdtgt0(xb))
    | ~ aElementOf0(sz00,slsdtgt0(xa)) ),
    inference(spt,[spt(split,[position(s2)])],[76]),
    [iquote('1:Spt:10303.0,76.1,76.2,76.3')] ).

cnf(10346,plain,
    ( ~ aElement0(xb)
    | ~ aElementOf0(xa,slsdtgt0(xa))
    | ~ aElementOf0(sz00,slsdtgt0(xa)) ),
    inference(res,[status(thm),theory(equality)],[8313,10338]),
    [iquote('1:Res:8313.1,10338.1')] ).

cnf(10347,plain,
    ( ~ aElementOf0(xa,slsdtgt0(xa))
    | ~ aElementOf0(sz00,slsdtgt0(xa)) ),
    inference(ssi,[status(thm)],[10346,4]),
    [iquote('1:SSi:10346.0,4.0')] ).

cnf(11147,plain,
    ( ~ aElement0(xa)
    | ~ aElementOf0(xa,slsdtgt0(xa)) ),
    inference(res,[status(thm),theory(equality)],[8313,10347]),
    [iquote('1:Res:8313.1,10347.1')] ).

cnf(11148,plain,
    ~ aElementOf0(xa,slsdtgt0(xa)),
    inference(ssi,[status(thm)],[11147,3]),
    [iquote('1:SSi:11147.0,3.0')] ).

cnf(11163,plain,
    ( ~ aElement0(xa)
    | ~ equal(xa,xa) ),
    inference(res,[status(thm),theory(equality)],[9274,11148]),
    [iquote('1:Res:9274.2,11148.0')] ).

cnf(11165,plain,
    ~ aElement0(xa),
    inference(obv,[status(thm),theory(equality)],[11163]),
    [iquote('1:Obv:11163.1')] ).

cnf(11166,plain,
    $false,
    inference(ssi,[status(thm)],[11165,3]),
    [iquote('1:SSi:11165.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : RNG108+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n021.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 19:27:14 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 3.55/3.77  
% 3.55/3.77  SPASS V 3.9 
% 3.55/3.77  SPASS beiseite: Proof found.
% 3.55/3.77  % SZS status Theorem
% 3.55/3.77  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 3.55/3.77  SPASS derived 6799 clauses, backtracked 381 clauses, performed 11 splits and kept 2540 clauses.
% 3.55/3.77  SPASS allocated 107645 KBytes.
% 3.55/3.77  SPASS spent	0:00:02.66 on the problem.
% 3.55/3.77  		0:00:00.03 for the input.
% 3.55/3.77  		0:00:00.12 for the FLOTTER CNF translation.
% 3.55/3.77  		0:00:00.08 for inferences.
% 3.55/3.77  		0:00:00.03 for the backtracking.
% 3.55/3.77  		0:00:02.34 for the reduction.
% 3.55/3.77  
% 3.55/3.77  
% 3.55/3.77  Here is a proof with depth 7, length 55 :
% 3.55/3.77  % SZS output start Refutation
% See solution above
% 3.55/3.77  Formulae used in the proof : mSortsC mSortsC_01 m__2091 mUnNeZr m__2129 mDefIdeal mPrIdeal mMulUnit mMulZero mEOfElem mDefDvs mDefPrIdeal mDefGCD m__
% 3.55/3.77  
%------------------------------------------------------------------------------