TSTP Solution File: RNG118+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG118+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 20:41:31 EDT 2022
% Result : Theorem 147.73s 147.95s
% Output : Refutation 147.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 27
% Syntax : Number of clauses : 73 ( 15 unt; 3 nHn; 73 RR)
% Number of literals : 227 ( 0 equ; 162 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
aElement0(sz00),
file('RNG118+1.p',unknown),
[] ).
cnf(3,axiom,
aElement0(xa),
file('RNG118+1.p',unknown),
[] ).
cnf(4,axiom,
aElement0(xb),
file('RNG118+1.p',unknown),
[] ).
cnf(5,axiom,
aIdeal0(xI),
file('RNG118+1.p',unknown),
[] ).
cnf(9,axiom,
aElementOf0(xu,xI),
file('RNG118+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(sz00,sz10),
file('RNG118+1.p',unknown),
[] ).
cnf(13,axiom,
aElement0(skf28(u,v)),
file('RNG118+1.p',unknown),
[] ).
cnf(18,axiom,
aElementOf0(sz00,slsdtgt0(xa)),
file('RNG118+1.p',unknown),
[] ).
cnf(21,axiom,
aElementOf0(xb,slsdtgt0(xb)),
file('RNG118+1.p',unknown),
[] ).
cnf(23,axiom,
~ equal(sz00,xu),
file('RNG118+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ aIdeal0(u)
| aSet0(u) ),
file('RNG118+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ aElement0(u)
| aIdeal0(slsdtgt0(u)) ),
file('RNG118+1.p',unknown),
[] ).
cnf(29,axiom,
equal(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)),xI),
file('RNG118+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ aElement0(u)
| equal(sdtpldt0(sz00,u),u) ),
file('RNG118+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ aElement0(u)
| equal(sdtasdt0(u,sz00),sz00) ),
file('RNG118+1.p',unknown),
[] ).
cnf(42,axiom,
( ~ aSet0(u)
| ~ aElementOf0(v,u)
| aElement0(v) ),
file('RNG118+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ aElement0(u)
| ~ equal(v,slsdtgt0(u))
| aSet0(v) ),
file('RNG118+1.p',unknown),
[] ).
cnf(59,axiom,
( iLess0(sbrdtbr0(skf27(u,v)),sbrdtbr0(u))
| equal(skf27(u,v),sz00) ),
file('RNG118+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| aElement0(skf27(u,v))
| equal(u,sz00) ),
file('RNG118+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ equal(w,sdtpldt1(v,u))
| aSet0(w) ),
file('RNG118+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ equal(u,sz00)
| ~ equal(sdtpldt0(sdtasdt0(v,xu),u),xb) ),
file('RNG118+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ aElementOf0(u,v)
| ~ aElementOf0(w,x)
| ~ equal(sdtpldt0(w,u),y)
| skP1(y,v,x) ),
file('RNG118+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ equal(w,slsdtgt0(u))
| ~ equal(sdtasdt0(u,v),x)
| aElementOf0(x,w) ),
file('RNG118+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| equal(u,sz00)
| equal(sdtpldt0(sdtasdt0(skf28(u,v),u),skf27(u,v)),v) ),
file('RNG118+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ equal(w,sdtpldt1(v,u))
| ~ skP1(x,u,v)
| aElementOf0(x,w) ),
file('RNG118+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ aElementOf0(w,x)
| ~ equal(x,sdtpldt1(v,u))
| skP1(w,u,v) ),
file('RNG118+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ aElement0(u)
| ~ aElement0(v)
| ~ iLess0(sbrdtbr0(u),sbrdtbr0(xu))
| ~ equal(sdtpldt0(sdtasdt0(v,xu),u),xb) ),
file('RNG118+1.p',unknown),
[] ).
cnf(186,plain,
( ~ aSet0(xI)
| aElement0(xu) ),
inference(res,[status(thm),theory(equality)],[9,42]),
[iquote('0:Res:9.0,42.1')] ).
cnf(194,plain,
aElement0(xu),
inference(ssi,[status(thm)],[186,25,5]),
[iquote('0:SSi:186.0,25.0,5.1')] ).
cnf(222,plain,
( ~ aElement0(u)
| aSet0(slsdtgt0(u)) ),
inference(eqr,[status(thm),theory(equality)],[55]),
[iquote('0:EqR:55.1')] ).
cnf(337,plain,
( ~ aSet0(u)
| ~ aSet0(v)
| aSet0(sdtpldt1(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[65]),
[iquote('0:EqR:65.2')] ).
cnf(340,plain,
( ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| aSet0(xI) ),
inference(spr,[status(thm),theory(equality)],[29,337]),
[iquote('0:SpR:29.0,337.2')] ).
cnf(341,plain,
aSet0(xI),
inference(ssi,[status(thm)],[340,28,3,222,4]),
[iquote('0:SSi:340.1,340.0,28.0,3.1,222.0,3.1,28.0,4.1,222.0,4.1')] ).
cnf(695,plain,
( ~ aElement0(u)
| ~ aElementOf0(u,v)
| ~ aElementOf0(sz00,w)
| ~ equal(u,x)
| skP1(x,v,w) ),
inference(spl,[status(thm),theory(equality)],[32,79]),
[iquote('0:SpL:32.1,79.2')] ).
cnf(832,plain,
( ~ aElement0(xu)
| ~ aElement0(u)
| ~ aElement0(skf27(xu,u))
| ~ aElement0(skf28(xu,u))
| ~ iLess0(sbrdtbr0(skf27(xu,u)),sbrdtbr0(xu))
| ~ equal(u,xb)
| equal(sz00,xu) ),
inference(spl,[status(thm),theory(equality)],[85,92]),
[iquote('0:SpL:85.3,92.3')] ).
cnf(833,plain,
( ~ aElement0(xu)
| ~ aElement0(u)
| ~ aElement0(skf27(xu,u))
| ~ aElement0(skf28(xu,u))
| ~ equal(skf27(xu,u),sz00)
| ~ equal(u,xb)
| equal(sz00,xu) ),
inference(spl,[status(thm),theory(equality)],[85,77]),
[iquote('0:SpL:85.3,77.3')] ).
cnf(839,plain,
( ~ aElement0(u)
| ~ aElement0(skf27(xu,u))
| ~ equal(skf27(xu,u),sz00)
| ~ equal(u,xb)
| equal(sz00,xu) ),
inference(ssi,[status(thm)],[833,13,194]),
[iquote('0:SSi:833.3,833.0,13.0,194.0,194.0')] ).
cnf(840,plain,
( ~ aElement0(u)
| ~ aElement0(skf27(xu,u))
| ~ equal(skf27(xu,u),sz00)
| ~ equal(u,xb) ),
inference(mrr,[status(thm)],[839,23]),
[iquote('0:MRR:839.4,23.0')] ).
cnf(842,plain,
( ~ aElement0(u)
| ~ aElement0(skf27(xu,u))
| ~ iLess0(sbrdtbr0(skf27(xu,u)),sbrdtbr0(xu))
| ~ equal(u,xb)
| equal(sz00,xu) ),
inference(ssi,[status(thm)],[832,13,194]),
[iquote('0:SSi:832.3,832.0,13.0,194.0,194.0')] ).
cnf(843,plain,
( ~ aElement0(u)
| ~ aElement0(skf27(xu,u))
| ~ iLess0(sbrdtbr0(skf27(xu,u)),sbrdtbr0(xu))
| ~ equal(u,xb) ),
inference(mrr,[status(thm)],[842,23]),
[iquote('0:MRR:842.4,23.0')] ).
cnf(1116,plain,
( ~ aElement0(u)
| ~ aElement0(u)
| ~ aElement0(sz00)
| ~ equal(v,slsdtgt0(u))
| ~ equal(sz00,w)
| aElementOf0(w,v) ),
inference(spl,[status(thm),theory(equality)],[35,84]),
[iquote('0:SpL:35.1,84.3')] ).
cnf(1123,plain,
( ~ aElement0(u)
| ~ aElement0(sz00)
| ~ equal(v,slsdtgt0(u))
| ~ equal(sz00,w)
| aElementOf0(w,v) ),
inference(obv,[status(thm),theory(equality)],[1116]),
[iquote('0:Obv:1116.0')] ).
cnf(1124,plain,
( ~ aElement0(u)
| ~ equal(v,slsdtgt0(u))
| ~ equal(sz00,w)
| aElementOf0(w,v) ),
inference(ssi,[status(thm)],[1123,1]),
[iquote('0:SSi:1123.1,1.0')] ).
cnf(1179,plain,
( ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| ~ aElementOf0(u,v)
| ~ equal(v,xI)
| skP1(u,slsdtgt0(xb),slsdtgt0(xa)) ),
inference(spl,[status(thm),theory(equality)],[29,89]),
[iquote('0:SpL:29.0,89.3')] ).
cnf(1180,plain,
( ~ aElementOf0(u,v)
| ~ equal(v,xI)
| skP1(u,slsdtgt0(xb),slsdtgt0(xa)) ),
inference(ssi,[status(thm)],[1179,28,3,222,4]),
[iquote('0:SSi:1179.1,1179.0,28.0,3.1,222.0,3.1,28.0,4.1,222.0,4.1')] ).
cnf(1214,plain,
( ~ aSet0(u)
| ~ aSet0(v)
| ~ skP1(w,u,v)
| aElementOf0(w,sdtpldt1(v,u)) ),
inference(eqr,[status(thm),theory(equality)],[88]),
[iquote('0:EqR:88.2')] ).
cnf(1215,plain,
( ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| ~ equal(u,xI)
| ~ skP1(v,slsdtgt0(xb),slsdtgt0(xa))
| aElementOf0(v,u) ),
inference(spl,[status(thm),theory(equality)],[29,88]),
[iquote('0:SpL:29.0,88.2')] ).
cnf(1216,plain,
( ~ equal(u,xI)
| ~ skP1(v,slsdtgt0(xb),slsdtgt0(xa))
| aElementOf0(v,u) ),
inference(ssi,[status(thm)],[1215,28,3,222,4]),
[iquote('0:SSi:1215.1,1215.0,28.0,3.1,222.0,3.1,28.0,4.1,222.0,4.1')] ).
cnf(4887,plain,
( ~ aElement0(u)
| ~ equal(sz00,v)
| aElementOf0(v,slsdtgt0(u)) ),
inference(eqr,[status(thm),theory(equality)],[1124]),
[iquote('0:EqR:1124.1')] ).
cnf(4892,plain,
( ~ aElement0(u)
| ~ aSet0(slsdtgt0(u))
| ~ equal(sz00,v)
| aElement0(v) ),
inference(res,[status(thm),theory(equality)],[4887,42]),
[iquote('0:Res:4887.2,42.1')] ).
cnf(4902,plain,
( ~ aElement0(u)
| ~ equal(sz00,v)
| aElement0(v) ),
inference(ssi,[status(thm)],[4892,28,222]),
[iquote('0:SSi:4892.1,28.1,222.1')] ).
cnf(4915,plain,
( ~ aElement0(u)
| ~ equal(skf27(xu,u),sz00)
| ~ equal(u,xb) ),
inference(mrr,[status(thm)],[840,4902]),
[iquote('0:MRR:840.1,4902.2')] ).
cnf(10383,plain,
( ~ aElement0(xb)
| ~ aElementOf0(sz00,u)
| ~ equal(xb,v)
| skP1(v,slsdtgt0(xb),u) ),
inference(res,[status(thm),theory(equality)],[21,695]),
[iquote('0:Res:21.0,695.1')] ).
cnf(10428,plain,
( ~ aElementOf0(sz00,u)
| ~ equal(xb,v)
| skP1(v,slsdtgt0(xb),u) ),
inference(ssi,[status(thm)],[10383,4]),
[iquote('0:SSi:10383.0,4.0')] ).
cnf(11121,plain,
( ~ aElement0(u)
| ~ aElement0(u)
| ~ aElement0(xu)
| ~ iLess0(sbrdtbr0(skf27(xu,u)),sbrdtbr0(xu))
| ~ equal(u,xb)
| equal(sz00,xu) ),
inference(sor,[status(thm)],[843,62]),
[iquote('0:SoR:843.1,62.2')] ).
cnf(11125,plain,
( ~ aElement0(u)
| ~ aElement0(xu)
| ~ iLess0(sbrdtbr0(skf27(xu,u)),sbrdtbr0(xu))
| ~ equal(u,xb)
| equal(sz00,xu) ),
inference(obv,[status(thm),theory(equality)],[11121]),
[iquote('0:Obv:11121.0')] ).
cnf(11126,plain,
( ~ aElement0(u)
| ~ iLess0(sbrdtbr0(skf27(xu,u)),sbrdtbr0(xu))
| ~ equal(u,xb)
| equal(sz00,xu) ),
inference(ssi,[status(thm)],[11125,194]),
[iquote('0:SSi:11125.1,194.0')] ).
cnf(11127,plain,
( ~ aElement0(u)
| ~ iLess0(sbrdtbr0(skf27(xu,u)),sbrdtbr0(xu))
| ~ equal(u,xb) ),
inference(mrr,[status(thm)],[11126,23]),
[iquote('0:MRR:11126.3,23.0')] ).
cnf(50100,plain,
( ~ aElementOf0(sz00,slsdtgt0(xa))
| ~ equal(xb,u)
| ~ equal(v,xI)
| aElementOf0(u,v) ),
inference(res,[status(thm),theory(equality)],[10428,1216]),
[iquote('0:Res:10428.2,1216.1')] ).
cnf(50103,plain,
( ~ equal(xb,u)
| ~ equal(v,xI)
| aElementOf0(u,v) ),
inference(mrr,[status(thm)],[50100,18]),
[iquote('0:MRR:50100.0,18.0')] ).
cnf(54504,plain,
( ~ equal(xb,u)
| ~ equal(v,xI)
| ~ equal(v,xI)
| skP1(u,slsdtgt0(xb),slsdtgt0(xa)) ),
inference(res,[status(thm),theory(equality)],[50103,1180]),
[iquote('0:Res:50103.2,1180.0')] ).
cnf(54550,plain,
( ~ equal(xb,u)
| ~ equal(v,xI)
| skP1(u,slsdtgt0(xb),slsdtgt0(xa)) ),
inference(obv,[status(thm),theory(equality)],[54504]),
[iquote('0:Obv:54504.1')] ).
cnf(54551,plain,
( ~ equal(xb,u)
| skP1(u,slsdtgt0(xb),slsdtgt0(xa)) ),
inference(aed,[status(thm),theory(equality)],[11,54550]),
[iquote('0:AED:11.0,54550.1')] ).
cnf(54671,plain,
( ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| ~ equal(xb,u)
| aElementOf0(u,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(res,[status(thm),theory(equality)],[54551,1214]),
[iquote('0:Res:54551.1,1214.2')] ).
cnf(54676,plain,
( ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa))
| ~ equal(xb,u)
| aElementOf0(u,xI) ),
inference(rew,[status(thm),theory(equality)],[29,54671]),
[iquote('0:Rew:29.0,54671.3')] ).
cnf(54677,plain,
( ~ equal(xb,u)
| aElementOf0(u,xI) ),
inference(ssi,[status(thm)],[54676,28,3,222,4]),
[iquote('0:SSi:54676.1,54676.0,28.0,3.1,222.0,3.1,28.0,4.1,222.0,4.1')] ).
cnf(54695,plain,
( ~ aSet0(xI)
| ~ equal(xb,u)
| aElement0(u) ),
inference(res,[status(thm),theory(equality)],[54677,42]),
[iquote('0:Res:54677.1,42.1')] ).
cnf(54718,plain,
( ~ equal(xb,u)
| aElement0(u) ),
inference(ssi,[status(thm)],[54695,5,341]),
[iquote('0:SSi:54695.0,5.0,341.0')] ).
cnf(54724,plain,
( ~ equal(skf27(xu,u),sz00)
| ~ equal(u,xb) ),
inference(mrr,[status(thm)],[4915,54718]),
[iquote('0:MRR:4915.0,54718.1')] ).
cnf(54760,plain,
( ~ iLess0(sbrdtbr0(skf27(xu,u)),sbrdtbr0(xu))
| ~ equal(u,xb) ),
inference(mrr,[status(thm)],[11127,54718]),
[iquote('0:MRR:11127.0,54718.1')] ).
cnf(55487,plain,
( ~ equal(u,xb)
| equal(skf27(xu,u),sz00) ),
inference(res,[status(thm),theory(equality)],[59,54760]),
[iquote('0:Res:59.0,54760.0')] ).
cnf(55488,plain,
~ equal(u,xb),
inference(mrr,[status(thm)],[55487,54724]),
[iquote('0:MRR:55487.1,54724.0')] ).
cnf(55489,plain,
$false,
inference(eqr,[status(thm),theory(equality)],[55488]),
[iquote('0:EqR:55488.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG118+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.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 16:29:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 147.73/147.95
% 147.73/147.95 SPASS V 3.9
% 147.73/147.95 SPASS beiseite: Proof found.
% 147.73/147.95 % SZS status Theorem
% 147.73/147.95 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 147.73/147.95 SPASS derived 32997 clauses, backtracked 0 clauses, performed 7 splits and kept 9516 clauses.
% 147.73/147.95 SPASS allocated 165756 KBytes.
% 147.73/147.95 SPASS spent 0:02:04.92 on the problem.
% 147.73/147.95 0:00:00.04 for the input.
% 147.73/147.95 0:00:00.13 for the FLOTTER CNF translation.
% 147.73/147.95 0:00:00.58 for inferences.
% 147.73/147.95 0:00:00.15 for the backtracking.
% 147.73/147.95 0:02:03.75 for the reduction.
% 147.73/147.95
% 147.73/147.95
% 147.73/147.95 Here is a proof with depth 6, length 73 :
% 147.73/147.95 % SZS output start Refutation
% See solution above
% 147.73/147.95 Formulae used in the proof : mSortsC m__2091 m__2174 m__2273 mUnNeZr mDivision mMulZero m__2416 m__2203 mDefIdeal mPrIdeal mAddZero mEOfElem mDefPrIdeal mDefSSum m__
% 147.73/147.95
%------------------------------------------------------------------------------