TSTP Solution File: SWC261-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC261-1 : 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 22:02:54 EDT 2022
% Result : Unsatisfiable 69.94s 70.14s
% Output : Refutation 69.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of clauses : 59 ( 15 unt; 12 nHn; 59 RR)
% Number of literals : 172 ( 0 equ; 109 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC261-1.p',unknown),
[] ).
cnf(2,axiom,
ssList(sk2),
file('SWC261-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC261-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ ssItem(u)
| ~ memberP(sk3,u)
| equal(sk5,u) ),
file('SWC261-1.p',unknown),
[] ).
cnf(9,axiom,
~ totalorderedP(sk1),
file('SWC261-1.p',unknown),
[] ).
cnf(36,axiom,
ssList(skaf68(u)),
file('SWC261-1.p',unknown),
[] ).
cnf(37,axiom,
ssList(skaf67(u)),
file('SWC261-1.p',unknown),
[] ).
cnf(38,axiom,
ssList(skaf66(u)),
file('SWC261-1.p',unknown),
[] ).
cnf(56,axiom,
ssItem(skaf44(u)),
file('SWC261-1.p',unknown),
[] ).
cnf(64,axiom,
( ~ ssItem(u)
| geq(u,u) ),
file('SWC261-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC261-1.p',unknown),
[] ).
cnf(94,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC261-1.p',unknown),
[] ).
cnf(95,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC261-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ ssList(u)
| ~ leq(skaf64(u),skaf65(u))
| totalorderedP(u) ),
file('SWC261-1.p',unknown),
[] ).
cnf(116,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ geq(u,v)
| leq(v,u) ),
file('SWC261-1.p',unknown),
[] ).
cnf(149,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ memberP(v,u)
| memberP(app(v,w),u) ),
file('SWC261-1.p',unknown),
[] ).
cnf(166,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC261-1.p',unknown),
[] ).
cnf(173,axiom,
( ~ ssList(u)
| totalorderedP(u)
| equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u) ),
file('SWC261-1.p',unknown),
[] ).
cnf(184,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ equal(app(w,cons(v,x)),u)
| memberP(u,v) ),
file('SWC261-1.p',unknown),
[] ).
cnf(188,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('SWC261-1.p',unknown),
[] ).
cnf(197,plain,
( ~ ssItem(u)
| ~ memberP(sk1,u)
| equal(sk5,u) ),
inference(rew,[status(thm),theory(equality)],[6,8]),
[iquote('0:Rew:6.0,8.1')] ).
cnf(442,plain,
( ~ ssItem(u)
| ssList(cons(u,sk2)) ),
inference(res,[status(thm),theory(equality)],[2,95]),
[iquote('0:Res:2.0,95.1')] ).
cnf(478,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[81]),
[iquote('1:Spt:81.1')] ).
cnf(480,plain,
geq(u,u),
inference(mrr,[status(thm)],[64,478]),
[iquote('1:MRR:64.0,478.0')] ).
cnf(507,plain,
( ~ memberP(sk1,u)
| equal(sk5,u) ),
inference(mrr,[status(thm)],[197,478]),
[iquote('1:MRR:197.0,478.0')] ).
cnf(524,plain,
( ~ geq(u,v)
| leq(v,u) ),
inference(mrr,[status(thm)],[116,478]),
[iquote('1:MRR:116.1,116.0,478.0')] ).
cnf(577,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ memberP(u,w)
| memberP(app(u,v),w) ),
inference(mrr,[status(thm)],[149,478]),
[iquote('1:MRR:149.0,478.0')] ).
cnf(614,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[95,478]),
[iquote('1:MRR:95.1,478.0')] ).
cnf(628,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(v,cons(x,w)),u)
| memberP(u,x) ),
inference(mrr,[status(thm)],[184,478]),
[iquote('1:MRR:184.1,478.0')] ).
cnf(1317,plain,
( ~ ssList(u)
| ~ geq(skaf65(u),skaf64(u))
| totalorderedP(u) ),
inference(res,[status(thm),theory(equality)],[524,100]),
[iquote('1:Res:524.1,100.1')] ).
cnf(3493,plain,
( ~ ssList(app(u,cons(v,w)))
| ~ ssList(u)
| ~ ssList(w)
| memberP(app(u,cons(v,w)),v) ),
inference(eqr,[status(thm),theory(equality)],[628]),
[iquote('1:EqR:628.3')] ).
cnf(3508,plain,
( ~ ssList(u)
| ~ ssList(v)
| memberP(app(u,cons(w,v)),w) ),
inference(ssi,[status(thm)],[3493,94,614]),
[iquote('1:SSi:3493.0,94.1,614.2')] ).
cnf(4177,plain,
( ~ ssList(u)
| ~ ssList(app(skaf66(u),cons(skaf64(u),skaf67(u))))
| ~ ssList(cons(skaf65(u),skaf68(u)))
| ~ memberP(app(skaf66(u),cons(skaf64(u),skaf67(u))),v)
| totalorderedP(u)
| memberP(u,v) ),
inference(spr,[status(thm),theory(equality)],[173,577]),
[iquote('1:SpR:173.2,577.3')] ).
cnf(4206,plain,
( ~ ssList(u)
| ~ memberP(app(skaf66(u),cons(skaf64(u),skaf67(u))),v)
| totalorderedP(u)
| memberP(u,v) ),
inference(ssi,[status(thm)],[4177,614,36,94,38,37]),
[iquote('1:SSi:4177.2,4177.1,614.0,36.1,94.0,38.2,614.0,37.1')] ).
cnf(6816,plain,
( ~ ssList(u)
| ~ ssList(app(skaf66(u),cons(skaf64(u),skaf67(u))))
| ~ ssList(skaf68(u))
| totalorderedP(u)
| memberP(u,skaf65(u)) ),
inference(spr,[status(thm),theory(equality)],[173,3508]),
[iquote('1:SpR:173.2,3508.2')] ).
cnf(6838,plain,
( ~ ssList(u)
| totalorderedP(u)
| memberP(u,skaf65(u)) ),
inference(ssi,[status(thm)],[6816,36,94,38,614,37]),
[iquote('1:SSi:6816.2,6816.1,36.0,94.1,38.0,614.2,37.0')] ).
cnf(7687,plain,
( ~ ssList(sk1)
| totalorderedP(sk1)
| equal(skaf65(sk1),sk5) ),
inference(res,[status(thm),theory(equality)],[6838,507]),
[iquote('1:Res:6838.2,507.0')] ).
cnf(23238,plain,
( ~ ssList(skaf66(u))
| ~ ssList(skaf67(u))
| ~ ssList(u)
| totalorderedP(u)
| memberP(u,skaf64(u)) ),
inference(res,[status(thm),theory(equality)],[3508,4206]),
[iquote('1:Res:3508.2,4206.1')] ).
cnf(23256,plain,
( ~ ssList(u)
| totalorderedP(u)
| memberP(u,skaf64(u)) ),
inference(ssi,[status(thm)],[23238,37,38]),
[iquote('1:SSi:23238.1,23238.0,37.0,38.0')] ).
cnf(31761,plain,
( ~ ssList(sk1)
| totalorderedP(sk1)
| equal(skaf64(sk1),sk5) ),
inference(res,[status(thm),theory(equality)],[23256,507]),
[iquote('1:Res:23256.2,507.0')] ).
cnf(32043,plain,
( totalorderedP(sk1)
| equal(skaf65(sk1),sk5) ),
inference(ssi,[status(thm)],[7687,1]),
[iquote('1:SSi:7687.0,1.0')] ).
cnf(32044,plain,
equal(skaf65(sk1),sk5),
inference(mrr,[status(thm)],[32043,9]),
[iquote('1:MRR:32043.0,9.0')] ).
cnf(32049,plain,
( totalorderedP(sk1)
| equal(skaf64(sk1),sk5) ),
inference(ssi,[status(thm)],[31761,1]),
[iquote('1:SSi:31761.0,1.0')] ).
cnf(32050,plain,
equal(skaf64(sk1),sk5),
inference(mrr,[status(thm)],[32049,9]),
[iquote('1:MRR:32049.0,9.0')] ).
cnf(32182,plain,
( ~ ssList(sk1)
| ~ geq(sk5,skaf64(sk1))
| totalorderedP(sk1) ),
inference(spl,[status(thm),theory(equality)],[32044,1317]),
[iquote('1:SpL:32044.0,1317.1')] ).
cnf(32188,plain,
( ~ ssList(sk1)
| ~ geq(sk5,sk5)
| totalorderedP(sk1) ),
inference(rew,[status(thm),theory(equality)],[32050,32182]),
[iquote('1:Rew:32050.0,32182.1')] ).
cnf(32189,plain,
( ~ geq(sk5,sk5)
| totalorderedP(sk1) ),
inference(ssi,[status(thm)],[32188,1]),
[iquote('1:SSi:32188.0,1.0')] ).
cnf(32190,plain,
$false,
inference(mrr,[status(thm)],[32189,480,9]),
[iquote('1:MRR:32189.0,32189.1,480.0,9.0')] ).
cnf(32203,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[81]),
[iquote('1:Spt:32190.0,81.0,81.2')] ).
cnf(32443,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)],[188,32203]),
[iquote('1:MRR:188.1,32203.1')] ).
cnf(46252,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)],[166,94]),
[iquote('0:SpR:166.3,94.2')] ).
cnf(46293,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[46252]),
[iquote('0:Obv:46252.0')] ).
cnf(46294,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[46293,95]),
[iquote('0:SSi:46293.2,95.2')] ).
cnf(47249,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)],[32443]),
[iquote('1:EqR:32443.5')] ).
cnf(47277,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[47249,94,95]),
[iquote('1:SSi:47249.0,94.2,94.2,95.2,95.2')] ).
cnf(47278,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[46294,47277]),
[iquote('1:MRR:46294.3,47277.1')] ).
cnf(47281,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[47278]),
[iquote('1:Con:47278.2')] ).
cnf(47282,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[442,47281]),
[iquote('1:MRR:442.1,47281.0')] ).
cnf(47283,plain,
$false,
inference(unc,[status(thm)],[47282,56]),
[iquote('1:UnC:47282.0,56.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC261-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 11 21:47:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 69.94/70.14
% 69.94/70.14 SPASS V 3.9
% 69.94/70.14 SPASS beiseite: Proof found.
% 69.94/70.14 % SZS status Theorem
% 69.94/70.14 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 69.94/70.14 SPASS derived 28677 clauses, backtracked 7658 clauses, performed 101 splits and kept 18125 clauses.
% 69.94/70.14 SPASS allocated 113758 KBytes.
% 69.94/70.14 SPASS spent 0:0:58.29 on the problem.
% 69.94/70.14 0:00:00.04 for the input.
% 69.94/70.14 0:00:00.00 for the FLOTTER CNF translation.
% 69.94/70.14 0:00:00.47 for inferences.
% 69.94/70.14 0:00:02.89 for the backtracking.
% 69.94/70.14 0:0:54.38 for the reduction.
% 69.94/70.14
% 69.94/70.14
% 69.94/70.14 Here is a proof with depth 4, length 59 :
% 69.94/70.14 % SZS output start Refutation
% See solution above
% 69.94/70.14 Formulae used in the proof : co1_1 co1_2 co1_6 co1_8 co1_9 clause27 clause28 clause29 clause47 clause55 clause72 clause85 clause86 clause91 clause107 clause140 clause157 clause164 clause175 clause179
% 69.94/70.14
%------------------------------------------------------------------------------