TSTP Solution File: SWC220-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC220-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 22:02:34 EDT 2022
% Result : Unsatisfiable 28.95s 29.16s
% Output : Refutation 28.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of clauses : 66 ( 18 unt; 9 nHn; 66 RR)
% Number of literals : 194 ( 0 equ; 133 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC220-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC220-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC220-1.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('SWC220-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(u,sk5(u,v,w)) ),
file('SWC220-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| leq(w,sk5(u,v,w)) ),
file('SWC220-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| ~ leq(sk5(u,v,w),w) ),
file('SWC220-1.p',unknown),
[] ).
cnf(14,axiom,
( equal(sk3,nil)
| ssList(sk7) ),
file('SWC220-1.p',unknown),
[] ).
cnf(15,axiom,
( equal(sk3,nil)
| ssList(sk8) ),
file('SWC220-1.p',unknown),
[] ).
cnf(16,axiom,
( equal(sk3,nil)
| equal(app(app(sk7,cons(sk6,nil)),sk8),sk3) ),
file('SWC220-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ ssItem(u)
| ~ memberP(sk7,u)
| ~ memberP(sk8,u)
| ~ leq(sk6,u)
| equal(sk3,nil)
| leq(u,sk6) ),
file('SWC220-1.p',unknown),
[] ).
cnf(64,axiom,
ssItem(skaf44(u)),
file('SWC220-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| leq(u,u) ),
file('SWC220-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC220-1.p',unknown),
[] ).
cnf(102,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC220-1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC220-1.p',unknown),
[] ).
cnf(147,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ leq(u,v)
| ~ leq(v,u)
| equal(u,v) ),
file('SWC220-1.p',unknown),
[] ).
cnf(174,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC220-1.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('SWC220-1.p',unknown),
[] ).
cnf(205,plain,
( equal(nil,sk1)
| ssList(sk8) ),
inference(rew,[status(thm),theory(equality)],[6,15]),
[iquote('0:Rew:6.0,15.0')] ).
cnf(206,plain,
ssList(sk8),
inference(mrr,[status(thm)],[205,7]),
[iquote('0:MRR:205.0,7.0')] ).
cnf(207,plain,
( equal(nil,sk1)
| ssList(sk7) ),
inference(rew,[status(thm),theory(equality)],[6,14]),
[iquote('0:Rew:6.0,14.0')] ).
cnf(208,plain,
ssList(sk7),
inference(mrr,[status(thm)],[207,7]),
[iquote('0:MRR:207.0,7.0')] ).
cnf(211,plain,
( equal(nil,sk1)
| equal(app(app(sk7,cons(sk6,nil)),sk8),sk1) ),
inference(rew,[status(thm),theory(equality)],[6,16]),
[iquote('0:Rew:6.0,16.1,6.0,16.0')] ).
cnf(212,plain,
equal(app(app(sk7,cons(sk6,nil)),sk8),sk1),
inference(mrr,[status(thm)],[211,7]),
[iquote('0:MRR:211.0,7.0')] ).
cnf(213,plain,
( ~ ssItem(u)
| ~ memberP(sk7,u)
| ~ memberP(sk8,u)
| ~ leq(sk6,u)
| equal(nil,sk1)
| leq(u,sk6) ),
inference(rew,[status(thm),theory(equality)],[6,17]),
[iquote('0:Rew:6.0,17.4')] ).
cnf(214,plain,
( ~ ssItem(u)
| ~ leq(sk6,u)
| ~ memberP(sk8,u)
| ~ memberP(sk7,u)
| leq(u,sk6) ),
inference(mrr,[status(thm)],[213,7]),
[iquote('0:MRR:213.4,7.0')] ).
cnf(542,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,103]),
[iquote('0:Res:1.0,103.1')] ).
cnf(599,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[89]),
[iquote('1:Spt:89.1')] ).
cnf(600,plain,
leq(u,u),
inference(mrr,[status(thm)],[79,599]),
[iquote('1:MRR:79.0,599.0')] ).
cnf(666,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(u,v) ),
inference(mrr,[status(thm)],[147,599]),
[iquote('1:MRR:147.1,147.0,599.0')] ).
cnf(682,plain,
( ~ leq(sk6,u)
| ~ memberP(sk8,u)
| ~ memberP(sk7,u)
| leq(u,sk6) ),
inference(mrr,[status(thm)],[214,599]),
[iquote('1:MRR:214.0,599.0')] ).
cnf(810,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| leq(w,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[11,599]),
[iquote('1:MRR:11.2,599.0')] ).
cnf(811,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(u,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[10,599]),
[iquote('1:MRR:10.2,599.0')] ).
cnf(812,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[9,599]),
[iquote('1:MRR:9.2,599.0')] ).
cnf(813,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| ~ leq(sk5(u,v,w),w) ),
inference(mrr,[status(thm)],[12,599]),
[iquote('1:MRR:12.2,599.0')] ).
cnf(9013,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk1,sk1)
| leq(sk6,sk5(sk8,sk7,sk6)) ),
inference(spl,[status(thm),theory(equality)],[212,810]),
[iquote('1:SpL:212.0,810.2')] ).
cnf(9016,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| leq(sk6,sk5(sk8,sk7,sk6)) ),
inference(obv,[status(thm),theory(equality)],[9013]),
[iquote('1:Obv:9013.2')] ).
cnf(9017,plain,
leq(sk6,sk5(sk8,sk7,sk6)),
inference(ssi,[status(thm)],[9016,208,206]),
[iquote('1:SSi:9016.1,9016.0,208.0,206.0')] ).
cnf(9045,plain,
( ~ leq(sk5(sk8,sk7,sk6),sk6)
| equal(sk5(sk8,sk7,sk6),sk6) ),
inference(res,[status(thm),theory(equality)],[9017,666]),
[iquote('1:Res:9017.0,666.0')] ).
cnf(9046,plain,
( ~ memberP(sk8,sk5(sk8,sk7,sk6))
| ~ memberP(sk7,sk5(sk8,sk7,sk6))
| leq(sk5(sk8,sk7,sk6),sk6) ),
inference(res,[status(thm),theory(equality)],[9017,682]),
[iquote('1:Res:9017.0,682.0')] ).
cnf(9217,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk1,sk1)
| memberP(sk8,sk5(sk8,sk7,sk6)) ),
inference(spl,[status(thm),theory(equality)],[212,811]),
[iquote('1:SpL:212.0,811.2')] ).
cnf(9220,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| memberP(sk8,sk5(sk8,sk7,sk6)) ),
inference(obv,[status(thm),theory(equality)],[9217]),
[iquote('1:Obv:9217.2')] ).
cnf(9221,plain,
memberP(sk8,sk5(sk8,sk7,sk6)),
inference(ssi,[status(thm)],[9220,208,206]),
[iquote('1:SSi:9220.1,9220.0,208.0,206.0')] ).
cnf(9222,plain,
( ~ memberP(sk7,sk5(sk8,sk7,sk6))
| leq(sk5(sk8,sk7,sk6),sk6) ),
inference(mrr,[status(thm)],[9046,9221]),
[iquote('1:MRR:9046.0,9221.0')] ).
cnf(9295,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk1,sk1)
| memberP(sk7,sk5(sk8,sk7,sk6)) ),
inference(spl,[status(thm),theory(equality)],[212,812]),
[iquote('1:SpL:212.0,812.2')] ).
cnf(9298,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| memberP(sk7,sk5(sk8,sk7,sk6)) ),
inference(obv,[status(thm),theory(equality)],[9295]),
[iquote('1:Obv:9295.2')] ).
cnf(10991,plain,
memberP(sk7,sk5(sk8,sk7,sk6)),
inference(ssi,[status(thm)],[9298,208,206]),
[iquote('1:SSi:9298.1,9298.0,208.0,206.0')] ).
cnf(10993,plain,
leq(sk5(sk8,sk7,sk6),sk6),
inference(mrr,[status(thm)],[9222,10991]),
[iquote('1:MRR:9222.0,10991.0')] ).
cnf(10994,plain,
equal(sk5(sk8,sk7,sk6),sk6),
inference(mrr,[status(thm)],[9045,10993]),
[iquote('1:MRR:9045.0,10993.0')] ).
cnf(11048,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk1,sk1)
| ~ leq(sk5(sk8,sk7,sk6),sk6) ),
inference(spl,[status(thm),theory(equality)],[212,813]),
[iquote('1:SpL:212.0,813.2')] ).
cnf(11063,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ leq(sk5(sk8,sk7,sk6),sk6) ),
inference(obv,[status(thm),theory(equality)],[11048]),
[iquote('1:Obv:11048.2')] ).
cnf(11064,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ leq(sk6,sk6) ),
inference(rew,[status(thm),theory(equality)],[10994,11063]),
[iquote('1:Rew:10994.0,11063.2')] ).
cnf(11065,plain,
~ leq(sk6,sk6),
inference(ssi,[status(thm)],[11064,208,206]),
[iquote('1:SSi:11064.1,11064.0,208.0,206.0')] ).
cnf(11066,plain,
$false,
inference(mrr,[status(thm)],[11065,600]),
[iquote('1:MRR:11065.0,600.0')] ).
cnf(11071,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[89]),
[iquote('1:Spt:11066.0,89.0,89.2')] ).
cnf(11100,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)],[196,11071]),
[iquote('1:MRR:196.1,11071.1')] ).
cnf(42527,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(42569,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[42527]),
[iquote('0:Obv:42527.0')] ).
cnf(42570,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[42569,103]),
[iquote('0:SSi:42569.2,103.2')] ).
cnf(44913,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)],[11100]),
[iquote('1:EqR:11100.5')] ).
cnf(44947,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[44913,102,103]),
[iquote('1:SSi:44913.0,102.2,102.2,103.2,103.2')] ).
cnf(44949,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[42570,44947]),
[iquote('1:MRR:42570.3,44947.1')] ).
cnf(44952,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[44949]),
[iquote('1:Con:44949.2')] ).
cnf(44954,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[542,44952]),
[iquote('1:MRR:542.1,44952.0')] ).
cnf(44958,plain,
$false,
inference(unc,[status(thm)],[44954,64]),
[iquote('1:UnC:44954.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC220-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 12 20:21:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 28.95/29.16
% 28.95/29.16 SPASS V 3.9
% 28.95/29.16 SPASS beiseite: Proof found.
% 28.95/29.16 % SZS status Theorem
% 28.95/29.16 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.95/29.16 SPASS derived 32221 clauses, backtracked 6534 clauses, performed 87 splits and kept 18982 clauses.
% 28.95/29.16 SPASS allocated 107150 KBytes.
% 28.95/29.16 SPASS spent 0:0:21.09 on the problem.
% 28.95/29.16 0:00:00.05 for the input.
% 28.95/29.16 0:00:00.00 for the FLOTTER CNF translation.
% 28.95/29.16 0:00:00.33 for inferences.
% 28.95/29.16 0:00:00.81 for the backtracking.
% 28.95/29.16 0:0:19.46 for the reduction.
% 28.95/29.16
% 28.95/29.16
% 28.95/29.16 Here is a proof with depth 2, length 66 :
% 28.95/29.16 % SZS output start Refutation
% See solution above
% 28.95/29.16 Formulae used in the proof : co1_1 co1_6 co1_7 co1_9 co1_10 co1_11 co1_12 co1_14 co1_15 co1_16 co1_17 clause47 clause62 clause72 clause85 clause86 clause130 clause157 clause179
% 28.95/29.16
%------------------------------------------------------------------------------