TSTP Solution File: SWC222-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC222-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 22:02:35 EDT 2022
% Result : Unsatisfiable 28.21s 28.43s
% Output : Refutation 28.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of clauses : 66 ( 27 unt; 3 nHn; 66 RR)
% Number of literals : 151 ( 0 equ; 95 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('SWC222-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC222-1.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('SWC222-1.p',unknown),
[] ).
cnf(18,axiom,
equalelemsP(nil),
file('SWC222-1.p',unknown),
[] ).
cnf(19,axiom,
duplicatefreeP(nil),
file('SWC222-1.p',unknown),
[] ).
cnf(20,axiom,
strictorderedP(nil),
file('SWC222-1.p',unknown),
[] ).
cnf(21,axiom,
totalorderedP(nil),
file('SWC222-1.p',unknown),
[] ).
cnf(22,axiom,
strictorderP(nil),
file('SWC222-1.p',unknown),
[] ).
cnf(23,axiom,
totalorderP(nil),
file('SWC222-1.p',unknown),
[] ).
cnf(24,axiom,
cyclefreeP(nil),
file('SWC222-1.p',unknown),
[] ).
cnf(25,axiom,
ssList(nil),
file('SWC222-1.p',unknown),
[] ).
cnf(30,axiom,
ssList(skaf82(u)),
file('SWC222-1.p',unknown),
[] ).
cnf(64,axiom,
ssItem(skaf44(u)),
file('SWC222-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC222-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC222-1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC222-1.p',unknown),
[] ).
cnf(102,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(126,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC222-1.p',unknown),
[] ).
cnf(133,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC222-1.p',unknown),
[] ).
cnf(137,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(app(cons(v,nil),u),cons(v,u)) ),
file('SWC222-1.p',unknown),
[] ).
cnf(174,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC222-1.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('SWC222-1.p',unknown),
[] ).
cnf(458,plain,
( equal(cons(skaf83(sk1),skaf82(sk1)),sk1)
| equal(nil,sk1) ),
inference(res,[status(thm),theory(equality)],[1,126]),
[iquote('0:Res:1.0,126.0')] ).
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(587,plain,
equal(cons(skaf83(sk1),skaf82(sk1)),sk1),
inference(mrr,[status(thm)],[458,7]),
[iquote('0:MRR:458.1,7.0')] ).
cnf(599,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[89]),
[iquote('1:Spt:89.1')] ).
cnf(604,plain,
~ memberP(nil,u),
inference(mrr,[status(thm)],[88,599]),
[iquote('1:MRR:88.0,599.0')] ).
cnf(605,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[87,599]),
[iquote('1:MRR:87.0,599.0')] ).
cnf(606,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[86,599]),
[iquote('1:MRR:86.0,599.0')] ).
cnf(607,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[85,599]),
[iquote('1:MRR:85.0,599.0')] ).
cnf(608,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[84,599]),
[iquote('1:MRR:84.0,599.0')] ).
cnf(609,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[83,599]),
[iquote('1:MRR:83.0,599.0')] ).
cnf(610,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[82,599]),
[iquote('1:MRR:82.0,599.0')] ).
cnf(611,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[81,599]),
[iquote('1:MRR:81.0,599.0')] ).
cnf(723,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[103,599]),
[iquote('1:MRR:103.1,599.0')] ).
cnf(728,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[133,599]),
[iquote('1:MRR:133.1,599.0')] ).
cnf(729,plain,
( ~ ssList(u)
| equal(app(cons(v,nil),u),cons(v,u)) ),
inference(mrr,[status(thm)],[137,599]),
[iquote('1:MRR:137.1,599.0')] ).
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(1721,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[728]),
[iquote('1:EqR:728.1')] ).
cnf(1722,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[1721,723,18,19,20,21,22,23,24,25,611,610,609,608,607,606,605]),
[iquote('1:SSi:1721.0,723.0,18.0,19.0,20.0,21.0,22.0,23.0,24.0,25.0,611.0,610.0,609.0,608.0,607.0,606.0,605.1')] ).
cnf(9226,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)],[91,812]),
[iquote('1:SpL:91.1,812.2')] ).
cnf(9239,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)],[729,9226]),
[iquote('1:Rew:729.1,9226.3')] ).
cnf(9240,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[9239,25,24,23,22,21,20,19,18,723,1722,605,606,607,608,609,610,611]),
[iquote('1:SSi:9239.2,9239.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.0,723.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.1,1722.0,605.0,606.0,607.0,608.0,609.0,610.0,611.0')] ).
cnf(9241,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[9240,604]),
[iquote('1:MRR:9240.2,604.0')] ).
cnf(11058,plain,
( ~ ssList(skaf82(sk1))
| ~ equal(sk1,sk1) ),
inference(spl,[status(thm),theory(equality)],[587,9241]),
[iquote('1:SpL:587.0,9241.1')] ).
cnf(11430,plain,
~ ssList(skaf82(sk1)),
inference(obv,[status(thm),theory(equality)],[11058]),
[iquote('1:Obv:11058.1')] ).
cnf(11431,plain,
$false,
inference(ssi,[status(thm)],[11430,30,1]),
[iquote('1:SSi:11430.0,30.0,1.0')] ).
cnf(11490,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[89]),
[iquote('1:Spt:11431.0,89.0,89.2')] ).
cnf(11514,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)],[196,11490]),
[iquote('1:MRR:196.1,11490.1')] ).
cnf(42633,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(42675,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[42633]),
[iquote('0:Obv:42633.0')] ).
cnf(42676,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[42675,103]),
[iquote('0:SSi:42675.2,103.2')] ).
cnf(44767,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)],[11514]),
[iquote('1:EqR:11514.5')] ).
cnf(44800,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[44767,102,103]),
[iquote('1:SSi:44767.0,102.2,102.2,103.2,103.2')] ).
cnf(44802,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[42676,44800]),
[iquote('1:MRR:42676.3,44800.1')] ).
cnf(44805,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[44802]),
[iquote('1:Con:44802.2')] ).
cnf(44807,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[542,44805]),
[iquote('1:MRR:542.1,44805.0')] ).
cnf(44811,plain,
$false,
inference(unc,[status(thm)],[44807,64]),
[iquote('1:UnC:44807.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC222-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.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 06:28:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 28.21/28.43
% 28.21/28.43 SPASS V 3.9
% 28.21/28.43 SPASS beiseite: Proof found.
% 28.21/28.43 % SZS status Theorem
% 28.21/28.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.21/28.43 SPASS derived 32001 clauses, backtracked 7271 clauses, performed 89 splits and kept 19254 clauses.
% 28.21/28.43 SPASS allocated 106867 KBytes.
% 28.21/28.43 SPASS spent 0:0:20.31 on the problem.
% 28.21/28.43 0:00:00.04 for the input.
% 28.21/28.43 0:00:00.00 for the FLOTTER CNF translation.
% 28.21/28.43 0:00:00.31 for inferences.
% 28.21/28.43 0:00:00.77 for the backtracking.
% 28.21/28.43 0:0:18.77 for the reduction.
% 28.21/28.43
% 28.21/28.43
% 28.21/28.43 Here is a proof with depth 2, length 66 :
% 28.21/28.43 % SZS output start Refutation
% See solution above
% 28.21/28.43 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 clause120 clause157 clause179
% 28.21/28.43
%------------------------------------------------------------------------------