%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC237-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 22:02:42 EDT 2022
% Result : Unsatisfiable 16.64s 16.88s
% Output : Refutation 16.64s
% 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('SWC237-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC237-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC237-1.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('SWC237-1.p',unknown),
[] ).
cnf(18,axiom,
equalelemsP(nil),
file('SWC237-1.p',unknown),
[] ).
cnf(19,axiom,
duplicatefreeP(nil),
file('SWC237-1.p',unknown),
[] ).
cnf(20,axiom,
strictorderedP(nil),
file('SWC237-1.p',unknown),
[] ).
cnf(21,axiom,
totalorderedP(nil),
file('SWC237-1.p',unknown),
[] ).
cnf(22,axiom,
strictorderP(nil),
file('SWC237-1.p',unknown),
[] ).
cnf(23,axiom,
totalorderP(nil),
file('SWC237-1.p',unknown),
[] ).
cnf(24,axiom,
cyclefreeP(nil),
file('SWC237-1.p',unknown),
[] ).
cnf(25,axiom,
ssList(nil),
file('SWC237-1.p',unknown),
[] ).
cnf(30,axiom,
ssList(skaf82(u)),
file('SWC237-1.p',unknown),
[] ).
cnf(64,axiom,
ssItem(skaf44(u)),
file('SWC237-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC237-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC237-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC237-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC237-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC237-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC237-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC237-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC237-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC237-1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC237-1.p',unknown),
[] ).
cnf(102,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC237-1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC237-1.p',unknown),
[] ).
cnf(126,axiom,
( ~ ssList(u)
| equal(nil,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
file('SWC237-1.p',unknown),
[] ).
cnf(133,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC237-1.p',unknown),
[] ).
cnf(174,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC237-1.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('SWC237-1.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(708,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[103,581]),
[iquote('1:MRR:103.1,581.0')] ).
cnf(713,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[133,581]),
[iquote('1:MRR:133.1,581.0')] ).
cnf(794,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(3191,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[713]),
[iquote('1:EqR:713.1')] ).
cnf(3192,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[3191,708,25,24,23,22,21,20,19,18,593,592,591,590,589,588,587]),
[iquote('1:SSi:3191.0,708.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.0,593.0,592.0,591.0,590.0,589.0,588.0,587.1')] ).
cnf(6770,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(6783,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)],[91,6770,794]),
[iquote('1:Rew:91.1,6770.3,794.2,6770.3')] ).
cnf(6784,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1)
| memberP(nil,sk5(u,nil,v)) ),
inference(ssi,[status(thm)],[6783,25,24,23,22,21,20,19,18,708,593,592,591,590,589,588,587,3192]),
[iquote('1:SSi:6783.2,6783.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.0,708.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,18.1,593.0,592.0,591.0,590.0,589.0,588.0,587.0,3192.0')] ).
cnf(6785,plain,
( ~ ssList(u)
| ~ equal(cons(v,u),sk1) ),
inference(mrr,[status(thm)],[6784,586]),
[iquote('1:MRR:6784.2,586.0')] ).
cnf(7785,plain,
( ~ ssList(u)
| ~ ssList(skaf82(u))
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(spl,[status(thm),theory(equality)],[126,6785]),
[iquote('1:SpL:126.2,6785.1')] ).
cnf(7796,plain,
( ~ ssList(u)
| ~ equal(u,sk1)
| equal(nil,u) ),
inference(ssi,[status(thm)],[7785,30]),
[iquote('1:SSi:7785.1,30.0')] ).
cnf(9674,plain,
( ~ equal(sk1,sk1)
| equal(nil,sk1) ),
inference(ems,[status(thm)],[7796,1]),
[iquote('1:EmS:7796.0,1.0')] ).
cnf(9675,plain,
equal(nil,sk1),
inference(obv,[status(thm),theory(equality)],[9674]),
[iquote('1:Obv:9674.0')] ).
cnf(9676,plain,
$false,
inference(mrr,[status(thm)],[9675,7]),
[iquote('1:MRR:9675.0,7.0')] ).
cnf(9750,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[89]),
[iquote('1:Spt:9676.0,89.0,89.2')] ).
cnf(9797,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)],[196,9750]),
[iquote('1:MRR:196.1,9750.1')] ).
cnf(27055,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(27111,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[27055]),
[iquote('0:Obv:27055.0')] ).
cnf(27112,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[27111,103]),
[iquote('0:SSi:27111.2,103.2')] ).
cnf(28767,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)],[9797]),
[iquote('1:EqR:9797.5')] ).
cnf(28797,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[28767,102,103]),
[iquote('1:SSi:28767.0,102.2,102.2,103.2,103.2')] ).
cnf(28799,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[27112,28797]),
[iquote('1:MRR:27112.3,28797.1')] ).
cnf(28802,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[28799]),
[iquote('1:Con:28799.2')] ).
cnf(28804,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[539,28802]),
[iquote('1:MRR:539.1,28802.0')] ).
cnf(28807,plain,
$false,
inference(unc,[status(thm)],[28804,64]),
[iquote('1:UnC:28804.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SWC237-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.10 % Command : run_spass %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Sat Jun 11 23:54:10 EDT 2022
% 0.10/0.30 % CPUTime :
% 16.64/16.88
% 16.64/16.88 SPASS V 3.9
% 16.64/16.88 SPASS beiseite: Proof found.
% 16.64/16.88 % SZS status Theorem
% 16.64/16.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.64/16.88 SPASS derived 19295 clauses, backtracked 6511 clauses, performed 91 splits and kept 14650 clauses.
% 16.64/16.88 SPASS allocated 96461 KBytes.
% 16.64/16.88 SPASS spent 0:0:12.90 on the problem.
% 16.64/16.88 0:00:00.03 for the input.
% 16.64/16.88 0:00:00.00 for the FLOTTER CNF translation.
% 16.64/16.88 0:00:00.19 for inferences.
% 16.64/16.88 0:00:00.39 for the backtracking.
% 16.64/16.88 0:0:12.01 for the reduction.
% 16.64/16.88
% 16.64/16.88
% 16.64/16.88 Here is a proof with depth 3, length 66 :
% 16.64/16.88 % SZS output start Refutation
% See solution above
% 16.64/16.88 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
% 16.64/16.88
%------------------------------------------------------------------------------