TSTP Solution File: SWC224-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC224-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 : Tue Jul 19 22:02:36 EDT 2022
% Result : Unsatisfiable 16.80s 16.97s
% Output : Refutation 16.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of clauses : 66 ( 27 unt; 2 nHn; 66 RR)
% Number of literals : 154 ( 0 equ; 97 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC224-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC224-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC224-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(18,axiom,
equalelemsP(nil),
file('SWC224-1.p',unknown),
[] ).
cnf(19,axiom,
duplicatefreeP(nil),
file('SWC224-1.p',unknown),
[] ).
cnf(20,axiom,
strictorderedP(nil),
file('SWC224-1.p',unknown),
[] ).
cnf(21,axiom,
totalorderedP(nil),
file('SWC224-1.p',unknown),
[] ).
cnf(22,axiom,
strictorderP(nil),
file('SWC224-1.p',unknown),
[] ).
cnf(23,axiom,
totalorderP(nil),
file('SWC224-1.p',unknown),
[] ).
cnf(24,axiom,
cyclefreeP(nil),
file('SWC224-1.p',unknown),
[] ).
cnf(25,axiom,
ssList(nil),
file('SWC224-1.p',unknown),
[] ).
cnf(30,axiom,
ssList(skaf82(u)),
file('SWC224-1.p',unknown),
[] ).
cnf(64,axiom,
ssItem(skaf44(u)),
file('SWC224-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC224-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC224-1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC224-1.p',unknown),
[] ).
cnf(102,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC224-1.p',unknown),
[] ).
cnf(126,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC224-1.p',unknown),
[] ).
cnf(133,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC224-1.p',unknown),
[] ).
cnf(174,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC224-1.p',unknown),
[] ).
cnf(196,axiom,
( ~ ssList(u)
| ~ duplicatefreeP(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
file('SWC224-1.p',unknown),
[] ).
cnf(539,plain,
( ~ ssItem(u)
| ssList(cons(u,sk2)) ),
inference(res,[status(thm),theory(equality)],[2,103]),
[iquote('0:Res:2.0,103.1')] ).
cnf(581,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[89]),
[iquote('1:Spt:89.1')] ).
cnf(586,plain,
~ memberP(nil,u),
inference(mrr,[status(thm)],[88,581]),
[iquote('1:MRR:88.0,581.0')] ).
cnf(587,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[87,581]),
[iquote('1:MRR:87.0,581.0')] ).
cnf(588,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[86,581]),
[iquote('1:MRR:86.0,581.0')] ).
cnf(589,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[85,581]),
[iquote('1:MRR:85.0,581.0')] ).
cnf(590,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[84,581]),
[iquote('1:MRR:84.0,581.0')] ).
cnf(591,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[83,581]),
[iquote('1:MRR:83.0,581.0')] ).
cnf(592,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[82,581]),
[iquote('1:MRR:82.0,581.0')] ).
cnf(593,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[81,581]),
[iquote('1:MRR:81.0,581.0')] ).
cnf(706,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[103,581]),
[iquote('1:MRR:103.1,581.0')] ).
cnf(711,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[133,581]),
[iquote('1:MRR:133.1,581.0')] ).
cnf(793,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[174,581]),
[iquote('1:MRR:174.2,581.0')] ).
cnf(799,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[9,581]),
[iquote('1:MRR:9.2,581.0')] ).
cnf(3216,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[711]),
[iquote('1:EqR:711.1')] ).
cnf(3217,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[3216,706,25,24,23,22,21,20,19,18,593,592,591,590,589,588,587]),
[iquote('1:SSi:3216.0,706.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.0,593.0,592.0,591.0,590.0,589.0,588.0,587.1')] ).
cnf(7020,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ equal(app(cons(u,nil),v),sk1)
| memberP(nil,sk5(v,nil,u)) ),
inference(spl,[status(thm),theory(equality)],[91,799]),
[iquote('1:SpL:91.1,799.2')] ).
cnf(7033,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| ~ ssList(nil)
| ~ equal(cons(u,v),sk1)
| memberP(nil,sk5(v,nil,u)) ),
inference(rew,[status(thm),theory(equality)],[91,7020,793]),
[iquote('1:Rew:91.1,7020.3,793.2,7020.3')] ).
cnf(7034,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[7033,25,24,23,22,21,20,19,18,706,593,592,591,590,589,588,587,3217]),
[iquote('1:SSi:7033.2,7033.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.0,706.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.1,593.0,592.0,591.0,590.0,589.0,588.0,587.0,3217.0')] ).
cnf(7035,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[7034,586]),
[iquote('1:MRR:7034.2,586.0')] ).
cnf(8205,plain,
( ~ ssList(u)
| ~ ssList(skaf82(u))
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(spl,[status(thm),theory(equality)],[126,7035]),
[iquote('1:SpL:126.2,7035.1')] ).
cnf(8216,plain,
( ~ ssList(u)
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(ssi,[status(thm)],[8205,30]),
[iquote('1:SSi:8205.1,30.0')] ).
cnf(10308,plain,
( ~ equal(sk1,sk1)
| equal(nil,sk1) ),
inference(ems,[status(thm)],[8216,1]),
[iquote('1:EmS:8216.0,1.0')] ).
cnf(10309,plain,
equal(nil,sk1),
inference(obv,[status(thm),theory(equality)],[10308]),
[iquote('1:Obv:10308.0')] ).
cnf(10310,plain,
$false,
inference(mrr,[status(thm)],[10309,7]),
[iquote('1:MRR:10309.0,7.0')] ).
cnf(10384,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[89]),
[iquote('1:Spt:10310.0,89.0,89.2')] ).
cnf(10429,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssList(y)
| ~ equal(app(app(w,cons(v,x)),cons(v,y)),u) ),
inference(mrr,[status(thm)],[196,10384]),
[iquote('1:MRR:196.1,10384.1')] ).
cnf(28043,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ ssList(cons(w,v))
| ~ ssList(u)
| ssList(cons(w,app(v,u))) ),
inference(spr,[status(thm),theory(equality)],[174,102]),
[iquote('0:SpR:174.3,102.2')] ).
cnf(28099,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[28043]),
[iquote('0:Obv:28043.0')] ).
cnf(28100,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[28099,103]),
[iquote('0:SSi:28099.2,103.2')] ).
cnf(29917,plain,
( ~ ssList(app(app(u,cons(v,w)),cons(v,x)))
| ~ ssItem(v)
| ~ ssList(u)
| ~ ssList(w)
| ~ ssList(x) ),
inference(eqr,[status(thm),theory(equality)],[10429]),
[iquote('1:EqR:10429.5')] ).
cnf(29947,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[29917,102,103]),
[iquote('1:SSi:29917.0,102.2,102.2,103.2,103.2')] ).
cnf(29949,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[28100,29947]),
[iquote('1:MRR:28100.3,29947.1')] ).
cnf(29952,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[29949]),
[iquote('1:Con:29949.2')] ).
cnf(29954,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[539,29952]),
[iquote('1:MRR:539.1,29952.0')] ).
cnf(29957,plain,
$false,
inference(unc,[status(thm)],[29954,64]),
[iquote('1:UnC:29954.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC224-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 20:35:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 16.80/16.97
% 16.80/16.97 SPASS V 3.9
% 16.80/16.97 SPASS beiseite: Proof found.
% 16.80/16.97 % SZS status Theorem
% 16.80/16.97 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.80/16.97 SPASS derived 19992 clauses, backtracked 6564 clauses, performed 90 splits and kept 15237 clauses.
% 16.80/16.97 SPASS allocated 97259 KBytes.
% 16.80/16.97 SPASS spent 0:0:12.81 on the problem.
% 16.80/16.97 0:00:00.04 for the input.
% 16.80/16.97 0:00:00.00 for the FLOTTER CNF translation.
% 16.80/16.97 0:00:00.18 for inferences.
% 16.80/16.97 0:00:00.39 for the backtracking.
% 16.80/16.97 0:0:11.83 for the reduction.
% 16.80/16.97
% 16.80/16.97
% 16.80/16.97 Here is a proof with depth 3, length 66 :
% 16.80/16.97 % SZS output start Refutation
% See solution above
% 16.80/16.97 Formulae used in the proof : co1_1 co1_2 co1_7 co1_9 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause13 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause74 clause85 clause86 clause109 clause116 clause157 clause179
% 16.80/16.97
%------------------------------------------------------------------------------