TSTP Solution File: SWC012-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC012-1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Tue Jul 19 22:01:04 EDT 2022
% Result : Unsatisfiable 37.52s 37.71s
% Output : Refutation 37.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of clauses : 66 ( 28 unt; 2 nHn; 66 RR)
% Number of literals : 157 ( 0 equ; 105 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; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC012-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC012-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC012-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC012-1.p',unknown),
[] ).
cnf(7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('SWC012-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(v,w),sk1)
| ~ neq(sk4,nil) ),
file('SWC012-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ neq(sk4,nil)
| equal(app(sk3,cons(sk5,nil)),sk4) ),
file('SWC012-1.p',unknown),
[] ).
cnf(15,axiom,
equalelemsP(nil),
file('SWC012-1.p',unknown),
[] ).
cnf(16,axiom,
duplicatefreeP(nil),
file('SWC012-1.p',unknown),
[] ).
cnf(17,axiom,
strictorderedP(nil),
file('SWC012-1.p',unknown),
[] ).
cnf(18,axiom,
totalorderedP(nil),
file('SWC012-1.p',unknown),
[] ).
cnf(19,axiom,
strictorderP(nil),
file('SWC012-1.p',unknown),
[] ).
cnf(20,axiom,
totalorderP(nil),
file('SWC012-1.p',unknown),
[] ).
cnf(21,axiom,
cyclefreeP(nil),
file('SWC012-1.p',unknown),
[] ).
cnf(22,axiom,
ssList(nil),
file('SWC012-1.p',unknown),
[] ).
cnf(61,axiom,
ssItem(skaf44(u)),
file('SWC012-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC012-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC012-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC012-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC012-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC012-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC012-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC012-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC012-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssList(u)
| equal(app(u,nil),u) ),
file('SWC012-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC012-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC012-1.p',unknown),
[] ).
cnf(130,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC012-1.p',unknown),
[] ).
cnf(171,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC012-1.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('SWC012-1.p',unknown),
[] ).
cnf(204,plain,
neq(sk2,nil),
inference(obv,[status(thm),theory(equality)],[7]),
[iquote('0:Obv:7.0')] ).
cnf(205,plain,
( ~ neq(sk2,nil)
| equal(app(sk1,cons(sk5,nil)),sk2) ),
inference(rew,[status(thm),theory(equality)],[6,14,5]),
[iquote('0:Rew:6.0,14.1,5.0,14.1,5.0,14.0')] ).
cnf(206,plain,
equal(app(sk1,cons(sk5,nil)),sk2),
inference(mrr,[status(thm)],[205,204]),
[iquote('0:MRR:205.0,204.0')] ).
cnf(211,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(v,w),sk1)
| ~ neq(sk2,nil) ),
inference(rew,[status(thm),theory(equality)],[5,12]),
[iquote('0:Rew:5.0,12.5')] ).
cnf(212,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(v,u),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
inference(mrr,[status(thm)],[211,204]),
[iquote('0:MRR:211.5,204.0')] ).
cnf(351,plain,
( ~ ssItem(u)
| ssList(cons(u,sk2)) ),
inference(res,[status(thm),theory(equality)],[2,100]),
[iquote('0:Res:2.0,100.1')] ).
cnf(563,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[86]),
[iquote('1:Spt:86.1')] ).
cnf(569,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[84,563]),
[iquote('1:MRR:84.0,563.0')] ).
cnf(570,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[83,563]),
[iquote('1:MRR:83.0,563.0')] ).
cnf(571,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[82,563]),
[iquote('1:MRR:82.0,563.0')] ).
cnf(572,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[81,563]),
[iquote('1:MRR:81.0,563.0')] ).
cnf(573,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[80,563]),
[iquote('1:MRR:80.0,563.0')] ).
cnf(574,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[79,563]),
[iquote('1:MRR:79.0,563.0')] ).
cnf(575,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[78,563]),
[iquote('1:MRR:78.0,563.0')] ).
cnf(688,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[100,563]),
[iquote('1:MRR:100.1,563.0')] ).
cnf(693,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[130,563]),
[iquote('1:MRR:130.1,563.0')] ).
cnf(763,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,u),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
inference(mrr,[status(thm)],[212,563]),
[iquote('1:MRR:212.2,563.0')] ).
cnf(3181,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[693]),
[iquote('1:EqR:693.1')] ).
cnf(3182,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[3181,688,22,21,20,19,18,17,16,15,569,570,571,572,573,574,575]),
[iquote('1:SSi:3181.0,688.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,569.0,570.0,571.0,572.0,573.0,574.0,575.1')] ).
cnf(6498,plain,
( ~ ssList(app(u,cons(v,nil)))
| ~ ssList(nil)
| ~ ssList(u)
| ~ equal(app(u,nil),sk1)
| ~ equal(app(u,cons(v,nil)),sk2) ),
inference(spl,[status(thm),theory(equality)],[87,763]),
[iquote('1:SpL:87.1,763.3')] ).
cnf(6507,plain,
( ~ ssList(app(u,cons(v,nil)))
| ~ ssList(nil)
| ~ ssList(u)
| ~ equal(u,sk1)
| ~ equal(app(u,cons(v,nil)),sk2) ),
inference(rew,[status(thm),theory(equality)],[87,6498]),
[iquote('1:Rew:87.1,6498.3')] ).
cnf(6508,plain,
( ~ ssList(u)
| ~ equal(u,sk1)
| ~ equal(app(u,cons(v,nil)),sk2) ),
inference(ssi,[status(thm)],[6507,22,21,20,19,18,17,16,15,99,688,569,570,571,572,573,574,575,3182]),
[iquote('1:SSi:6507.1,6507.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,15.0,99.0,688.0,22.0,21.0,20.0,19.0,18.0,17.0,16.1,15.2,569.0,570.0,571.0,572.0,573.0,574.0,575.0,3182.0')] ).
cnf(13665,plain,
( ~ ssList(sk1)
| ~ equal(sk1,sk1)
| ~ equal(sk2,sk2) ),
inference(spl,[status(thm),theory(equality)],[206,6508]),
[iquote('1:SpL:206.0,6508.2')] ).
cnf(14823,plain,
~ ssList(sk1),
inference(obv,[status(thm),theory(equality)],[13665]),
[iquote('1:Obv:13665.2')] ).
cnf(14824,plain,
$false,
inference(ssi,[status(thm)],[14823,1]),
[iquote('1:SSi:14823.0,1.0')] ).
cnf(15022,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[86]),
[iquote('1:Spt:14824.0,86.0,86.2')] ).
cnf(15085,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)],[193,15022]),
[iquote('1:MRR:193.1,15022.1')] ).
cnf(41521,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(41569,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[41521]),
[iquote('0:Obv:41521.0')] ).
cnf(41570,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[41569,100]),
[iquote('0:SSi:41569.2,100.2')] ).
cnf(42656,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)],[15085]),
[iquote('1:EqR:15085.5')] ).
cnf(42688,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[42656,99,100]),
[iquote('1:SSi:42656.0,99.2,99.2,100.2,100.2')] ).
cnf(42689,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[41570,42688]),
[iquote('1:MRR:41570.3,42688.1')] ).
cnf(42692,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[42689]),
[iquote('1:Con:42689.2')] ).
cnf(42694,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[351,42692]),
[iquote('1:MRR:351.1,42692.0')] ).
cnf(42696,plain,
$false,
inference(unc,[status(thm)],[42694,61]),
[iquote('1:UnC:42694.0,61.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC012-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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 08:04:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 37.52/37.71
% 37.52/37.71 SPASS V 3.9
% 37.52/37.71 SPASS beiseite: Proof found.
% 37.52/37.71 % SZS status Theorem
% 37.52/37.71 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.52/37.71 SPASS derived 26130 clauses, backtracked 15497 clauses, performed 119 splits and kept 24565 clauses.
% 37.52/37.71 SPASS allocated 105882 KBytes.
% 37.52/37.71 SPASS spent 0:0:29.11 on the problem.
% 37.52/37.71 0:00:00.04 for the input.
% 37.52/37.71 0:00:00.00 for the FLOTTER CNF translation.
% 37.52/37.71 0:00:00.33 for inferences.
% 37.52/37.71 0:00:01.06 for the backtracking.
% 37.52/37.71 0:0:27.17 for the reduction.
% 37.52/37.71
% 37.52/37.71
% 37.52/37.71 Here is a proof with depth 2, length 66 :
% 37.52/37.71 % SZS output start Refutation
% See solution above
% 37.52/37.71 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_12 co1_14 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause85 clause86 clause116 clause157 clause179
% 37.52/37.71
%------------------------------------------------------------------------------