TSTP Solution File: SWC223-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC223-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 12.01s 12.24s
% Output : Refutation 12.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 29
% Syntax : Number of clauses : 65 ( 27 unt; 3 nHn; 65 RR)
% Number of literals : 149 ( 0 equ; 94 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 : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC223-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC223-1.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('SWC223-1.p',unknown),
[] ).
cnf(15,axiom,
equalelemsP(nil),
file('SWC223-1.p',unknown),
[] ).
cnf(16,axiom,
duplicatefreeP(nil),
file('SWC223-1.p',unknown),
[] ).
cnf(17,axiom,
strictorderedP(nil),
file('SWC223-1.p',unknown),
[] ).
cnf(18,axiom,
totalorderedP(nil),
file('SWC223-1.p',unknown),
[] ).
cnf(19,axiom,
strictorderP(nil),
file('SWC223-1.p',unknown),
[] ).
cnf(20,axiom,
totalorderP(nil),
file('SWC223-1.p',unknown),
[] ).
cnf(21,axiom,
cyclefreeP(nil),
file('SWC223-1.p',unknown),
[] ).
cnf(22,axiom,
ssList(nil),
file('SWC223-1.p',unknown),
[] ).
cnf(27,axiom,
ssList(skaf82(u)),
file('SWC223-1.p',unknown),
[] ).
cnf(61,axiom,
ssItem(skaf44(u)),
file('SWC223-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC223-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC223-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC223-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC223-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC223-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC223-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC223-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC223-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC223-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC223-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC223-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC223-1.p',unknown),
[] ).
cnf(123,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC223-1.p',unknown),
[] ).
cnf(130,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC223-1.p',unknown),
[] ).
cnf(171,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC223-1.p',unknown),
[] ).
cnf(193,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('SWC223-1.p',unknown),
[] ).
cnf(451,plain,
( equal(cons(skaf83(sk1),skaf82(sk1)),sk1)
| equal(nil,sk1) ),
inference(res,[status(thm),theory(equality)],[1,123]),
[iquote('0:Res:1.0,123.0')] ).
cnf(537,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,100]),
[iquote('0:Res:1.0,100.1')] ).
cnf(584,plain,
equal(cons(skaf83(sk1),skaf82(sk1)),sk1),
inference(mrr,[status(thm)],[451,7]),
[iquote('0:MRR:451.1,7.0')] ).
cnf(596,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[86]),
[iquote('1:Spt:86.1')] ).
cnf(601,plain,
~ memberP(nil,u),
inference(mrr,[status(thm)],[85,596]),
[iquote('1:MRR:85.0,596.0')] ).
cnf(602,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[84,596]),
[iquote('1:MRR:84.0,596.0')] ).
cnf(603,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[83,596]),
[iquote('1:MRR:83.0,596.0')] ).
cnf(604,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[82,596]),
[iquote('1:MRR:82.0,596.0')] ).
cnf(605,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[81,596]),
[iquote('1:MRR:81.0,596.0')] ).
cnf(606,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[80,596]),
[iquote('1:MRR:80.0,596.0')] ).
cnf(607,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[79,596]),
[iquote('1:MRR:79.0,596.0')] ).
cnf(608,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[78,596]),
[iquote('1:MRR:78.0,596.0')] ).
cnf(729,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[100,596]),
[iquote('1:MRR:100.1,596.0')] ).
cnf(734,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[130,596]),
[iquote('1:MRR:130.1,596.0')] ).
cnf(813,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[171,596]),
[iquote('1:MRR:171.2,596.0')] ).
cnf(818,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| memberP(v,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[9,596]),
[iquote('1:MRR:9.2,596.0')] ).
cnf(1822,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[734]),
[iquote('1:EqR:734.1')] ).
cnf(1823,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[1822,729,15,16,17,18,19,20,21,22,608,607,606,605,604,603,602]),
[iquote('1:SSi:1822.0,729.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,608.0,607.0,606.0,605.0,604.0,603.0,602.1')] ).
cnf(4975,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)],[88,818]),
[iquote('1:SpL:88.1,818.2')] ).
cnf(4989,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)],[88,4975,813]),
[iquote('1:Rew:88.1,4975.3,813.2,4975.3')] ).
cnf(4990,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[4989,15,16,17,18,19,20,21,22,729,608,607,606,605,604,603,602,1823]),
[iquote('1:SSi:4989.2,4989.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,729.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,22.1,608.0,607.0,606.0,605.0,604.0,603.0,602.0,1823.0')] ).
cnf(4991,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[4990,601]),
[iquote('1:MRR:4990.2,601.0')] ).
cnf(5400,plain,
( ~ ssList(skaf82(sk1))
| ~ equal(sk1,sk1) ),
inference(spl,[status(thm),theory(equality)],[584,4991]),
[iquote('1:SpL:584.0,4991.1')] ).
cnf(5734,plain,
~ ssList(skaf82(sk1)),
inference(obv,[status(thm),theory(equality)],[5400]),
[iquote('1:Obv:5400.1')] ).
cnf(5735,plain,
$false,
inference(ssi,[status(thm)],[5734,27,1]),
[iquote('1:SSi:5734.0,27.0,1.0')] ).
cnf(5780,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[86]),
[iquote('1:Spt:5735.0,86.0,86.2')] ).
cnf(5791,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)],[193,5780]),
[iquote('1:MRR:193.1,5780.1')] ).
cnf(21435,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)],[171,99]),
[iquote('0:SpR:171.3,99.2')] ).
cnf(21486,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[21435]),
[iquote('0:Obv:21435.0')] ).
cnf(21487,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[21486,100]),
[iquote('0:SSi:21486.2,100.2')] ).
cnf(23790,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)],[5791]),
[iquote('1:EqR:5791.5')] ).
cnf(23829,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[23790,99,100]),
[iquote('1:SSi:23790.0,99.2,99.2,100.2,100.2')] ).
cnf(23831,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[21487,23829]),
[iquote('1:MRR:21487.3,23829.1')] ).
cnf(23834,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[23831]),
[iquote('1:Con:23831.2')] ).
cnf(23836,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[537,23834]),
[iquote('1:MRR:537.1,23834.0')] ).
cnf(23840,plain,
$false,
inference(unc,[status(thm)],[23836,61]),
[iquote('1:UnC:23836.0,61.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC223-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 11:14:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 12.01/12.24
% 12.01/12.24 SPASS V 3.9
% 12.01/12.24 SPASS beiseite: Proof found.
% 12.01/12.24 % SZS status Theorem
% 12.01/12.24 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.01/12.24 SPASS derived 15118 clauses, backtracked 5128 clauses, performed 83 splits and kept 11318 clauses.
% 12.01/12.24 SPASS allocated 93389 KBytes.
% 12.01/12.24 SPASS spent 0:00:09.54 on the problem.
% 12.01/12.24 0:00:00.04 for the input.
% 12.01/12.24 0:00:00.00 for the FLOTTER CNF translation.
% 12.01/12.24 0:00:00.15 for inferences.
% 12.01/12.24 0:00:00.28 for the backtracking.
% 12.01/12.24 0:00:08.79 for the reduction.
% 12.01/12.24
% 12.01/12.24
% 12.01/12.24 Here is a proof with depth 2, length 65 :
% 12.01/12.24 % SZS output start Refutation
% See solution above
% 12.01/12.24 Formulae used in the proof : co1_1 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
% 12.01/12.24
%------------------------------------------------------------------------------