TSTP Solution File: SWC245-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC245-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 22:02:46 EDT 2022
% Result : Unsatisfiable 16.54s 16.77s
% Output : Refutation 16.54s
% 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('SWC245-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC245-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC245-1.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('SWC245-1.p',unknown),
[] ).
cnf(18,axiom,
equalelemsP(nil),
file('SWC245-1.p',unknown),
[] ).
cnf(19,axiom,
duplicatefreeP(nil),
file('SWC245-1.p',unknown),
[] ).
cnf(20,axiom,
strictorderedP(nil),
file('SWC245-1.p',unknown),
[] ).
cnf(21,axiom,
totalorderedP(nil),
file('SWC245-1.p',unknown),
[] ).
cnf(22,axiom,
strictorderP(nil),
file('SWC245-1.p',unknown),
[] ).
cnf(23,axiom,
totalorderP(nil),
file('SWC245-1.p',unknown),
[] ).
cnf(24,axiom,
cyclefreeP(nil),
file('SWC245-1.p',unknown),
[] ).
cnf(25,axiom,
ssList(nil),
file('SWC245-1.p',unknown),
[] ).
cnf(30,axiom,
ssList(skaf82(u)),
file('SWC245-1.p',unknown),
[] ).
cnf(64,axiom,
ssItem(skaf44(u)),
file('SWC245-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC245-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC245-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC245-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC245-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC245-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC245-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC245-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC245-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC245-1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC245-1.p',unknown),
[] ).
cnf(102,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC245-1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC245-1.p',unknown),
[] ).
cnf(126,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC245-1.p',unknown),
[] ).
cnf(133,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC245-1.p',unknown),
[] ).
cnf(174,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC245-1.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('SWC245-1.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(3190,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[711]),
[iquote('1:EqR:711.1')] ).
cnf(3191,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[3190,706,25,24,23,22,21,20,19,18,593,592,591,590,589,588,587]),
[iquote('1:SSi:3190.0,706.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.0,593.0,592.0,591.0,590.0,589.0,588.0,587.1')] ).
cnf(6898,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(6911,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)],[91,6898,793]),
[iquote('1:Rew:91.1,6898.3,793.2,6898.3')] ).
cnf(6912,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[6911,25,24,23,22,21,20,19,18,706,593,592,591,590,589,588,587,3191]),
[iquote('1:SSi:6911.2,6911.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.0,706.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.1,593.0,592.0,591.0,590.0,589.0,588.0,587.0,3191.0')] ).
cnf(6913,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[6912,586]),
[iquote('1:MRR:6912.2,586.0')] ).
cnf(7653,plain,
( ~ ssList(u)
| ~ ssList(skaf82(u))
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(spl,[status(thm),theory(equality)],[126,6913]),
[iquote('1:SpL:126.2,6913.1')] ).
cnf(7664,plain,
( ~ ssList(u)
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(ssi,[status(thm)],[7653,30]),
[iquote('1:SSi:7653.1,30.0')] ).
cnf(9665,plain,
( ~ equal(sk1,sk1)
| equal(nil,sk1) ),
inference(ems,[status(thm)],[7664,1]),
[iquote('1:EmS:7664.0,1.0')] ).
cnf(9666,plain,
equal(nil,sk1),
inference(obv,[status(thm),theory(equality)],[9665]),
[iquote('1:Obv:9665.0')] ).
cnf(9667,plain,
$false,
inference(mrr,[status(thm)],[9666,7]),
[iquote('1:MRR:9666.0,7.0')] ).
cnf(9741,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[89]),
[iquote('1:Spt:9667.0,89.0,89.2')] ).
cnf(9788,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)],[196,9741]),
[iquote('1:MRR:196.1,9741.1')] ).
cnf(27363,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(27399,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[27363]),
[iquote('0:Obv:27363.0')] ).
cnf(27400,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[27399,103]),
[iquote('0:SSi:27399.2,103.2')] ).
cnf(28909,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)],[9788]),
[iquote('1:EqR:9788.5')] ).
cnf(28937,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[28909,102,103]),
[iquote('1:SSi:28909.0,102.2,102.2,103.2,103.2')] ).
cnf(28939,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[27400,28937]),
[iquote('1:MRR:27400.3,28937.1')] ).
cnf(28942,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[28939]),
[iquote('1:Con:28939.2')] ).
cnf(28944,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[539,28942]),
[iquote('1:MRR:539.1,28942.0')] ).
cnf(28947,plain,
$false,
inference(unc,[status(thm)],[28944,64]),
[iquote('1:UnC:28944.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC245-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n005.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 12:07:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 16.54/16.77
% 16.54/16.77 SPASS V 3.9
% 16.54/16.77 SPASS beiseite: Proof found.
% 16.54/16.77 % SZS status Theorem
% 16.54/16.77 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.54/16.77 SPASS derived 19364 clauses, backtracked 6461 clauses, performed 92 splits and kept 14710 clauses.
% 16.54/16.77 SPASS allocated 96648 KBytes.
% 16.54/16.77 SPASS spent 0:0:12.67 on the problem.
% 16.54/16.77 0:00:00.04 for the input.
% 16.54/16.77 0:00:00.00 for the FLOTTER CNF translation.
% 16.54/16.77 0:00:00.17 for inferences.
% 16.54/16.77 0:00:00.38 for the backtracking.
% 16.54/16.77 0:0:11.77 for the reduction.
% 16.54/16.77
% 16.54/16.77
% 16.54/16.77 Here is a proof with depth 3, length 66 :
% 16.54/16.77 % SZS output start Refutation
% See solution above
% 16.54/16.77 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
% 16.54/16.77
%------------------------------------------------------------------------------