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