TSTP Solution File: SWC419-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC419-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 22:03:57 EDT 2022
% Result : Unsatisfiable 41.32s 41.53s
% Output : Refutation 41.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 34
% Syntax : Number of clauses : 84 ( 30 unt; 1 nHn; 84 RR)
% Number of literals : 199 ( 0 equ; 131 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 : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC419-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC419-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC419-1.p',unknown),
[] ).
cnf(7,axiom,
neq(sk2,nil),
file('SWC419-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(u,cons(w,nil)),v),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
file('SWC419-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('SWC419-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ neq(sk4,nil)
| equal(app(cons(sk5,nil),sk6),sk4) ),
file('SWC419-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ neq(sk4,nil)
| equal(app(sk6,cons(sk5,nil)),sk3) ),
file('SWC419-1.p',unknown),
[] ).
cnf(14,axiom,
equalelemsP(nil),
file('SWC419-1.p',unknown),
[] ).
cnf(15,axiom,
duplicatefreeP(nil),
file('SWC419-1.p',unknown),
[] ).
cnf(16,axiom,
strictorderedP(nil),
file('SWC419-1.p',unknown),
[] ).
cnf(17,axiom,
totalorderedP(nil),
file('SWC419-1.p',unknown),
[] ).
cnf(18,axiom,
strictorderP(nil),
file('SWC419-1.p',unknown),
[] ).
cnf(19,axiom,
totalorderP(nil),
file('SWC419-1.p',unknown),
[] ).
cnf(20,axiom,
cyclefreeP(nil),
file('SWC419-1.p',unknown),
[] ).
cnf(21,axiom,
ssList(nil),
file('SWC419-1.p',unknown),
[] ).
cnf(60,axiom,
ssItem(skaf44(u)),
file('SWC419-1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC419-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssList(u)
| equal(app(u,nil),u) ),
file('SWC419-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC419-1.p',unknown),
[] ).
cnf(98,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(99,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(129,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC419-1.p',unknown),
[] ).
cnf(133,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(app(cons(v,nil),u),cons(v,u)) ),
file('SWC419-1.p',unknown),
[] ).
cnf(162,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(u,v),w),app(u,app(v,w))) ),
file('SWC419-1.p',unknown),
[] ).
cnf(170,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC419-1.p',unknown),
[] ).
cnf(192,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('SWC419-1.p',unknown),
[] ).
cnf(201,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(rew,[status(thm),theory(equality)],[5,11]),
[iquote('0:Rew:5.0,11.0')] ).
cnf(202,plain,
ssList(sk6),
inference(mrr,[status(thm)],[201,7]),
[iquote('0:MRR:201.0,7.0')] ).
cnf(206,plain,
( ~ neq(sk2,nil)
| equal(app(sk6,cons(sk5,nil)),sk1) ),
inference(rew,[status(thm),theory(equality)],[6,13,5]),
[iquote('0:Rew:6.0,13.1,5.0,13.0')] ).
cnf(207,plain,
equal(app(sk6,cons(sk5,nil)),sk1),
inference(mrr,[status(thm)],[206,7]),
[iquote('0:MRR:206.0,7.0')] ).
cnf(208,plain,
( ~ neq(sk2,nil)
| equal(app(cons(sk5,nil),sk6),sk2) ),
inference(rew,[status(thm),theory(equality)],[5,12]),
[iquote('0:Rew:5.0,12.1,5.0,12.0')] ).
cnf(209,plain,
equal(app(cons(sk5,nil),sk6),sk2),
inference(mrr,[status(thm)],[208,7]),
[iquote('0:MRR:208.0,7.0')] ).
cnf(525,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,99]),
[iquote('0:Res:1.0,99.1')] ).
cnf(569,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[85]),
[iquote('1:Spt:85.1')] ).
cnf(575,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[83,569]),
[iquote('1:MRR:83.0,569.0')] ).
cnf(576,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[82,569]),
[iquote('1:MRR:82.0,569.0')] ).
cnf(577,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[81,569]),
[iquote('1:MRR:81.0,569.0')] ).
cnf(578,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[80,569]),
[iquote('1:MRR:80.0,569.0')] ).
cnf(579,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[79,569]),
[iquote('1:MRR:79.0,569.0')] ).
cnf(580,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[78,569]),
[iquote('1:MRR:78.0,569.0')] ).
cnf(581,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[77,569]),
[iquote('1:MRR:77.0,569.0')] ).
cnf(694,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[99,569]),
[iquote('1:MRR:99.1,569.0')] ).
cnf(699,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[129,569]),
[iquote('1:MRR:129.1,569.0')] ).
cnf(700,plain,
( ~ ssList(u)
| equal(app(cons(v,nil),u),cons(v,u)) ),
inference(mrr,[status(thm)],[133,569]),
[iquote('1:MRR:133.1,569.0')] ).
cnf(766,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[170,569]),
[iquote('1:MRR:170.2,569.0')] ).
cnf(769,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(u,cons(w,nil)),v),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
inference(mrr,[status(thm)],[8,569]),
[iquote('1:MRR:8.2,569.0')] ).
cnf(1779,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[699]),
[iquote('1:EqR:699.1')] ).
cnf(1780,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[1779,694,14,15,16,17,18,19,20,21,581,580,579,578,577,576,575]),
[iquote('1:SSi:1779.0,694.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,581.0,580.0,579.0,578.0,577.0,576.0,575.1')] ).
cnf(1890,plain,
( ~ ssList(sk6)
| equal(cons(sk5,sk6),sk2) ),
inference(spr,[status(thm),theory(equality)],[700,209]),
[iquote('1:SpR:700.1,209.0')] ).
cnf(1901,plain,
equal(cons(sk5,sk6),sk2),
inference(ssi,[status(thm)],[1890,202]),
[iquote('1:SSi:1890.0,202.0')] ).
cnf(4029,plain,
( ~ ssList(u)
| ~ ssList(nil)
| ~ ssList(u)
| ~ ssList(v)
| equal(app(nil,app(u,v)),app(u,v)) ),
inference(spr,[status(thm),theory(equality)],[87,162]),
[iquote('0:SpR:87.1,162.3')] ).
cnf(4056,plain,
( ~ ssList(nil)
| ~ ssList(u)
| ~ ssList(v)
| equal(app(nil,app(u,v)),app(u,v)) ),
inference(obv,[status(thm),theory(equality)],[4029]),
[iquote('0:Obv:4029.0')] ).
cnf(4057,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(nil,app(u,v)),app(u,v)) ),
inference(ssi,[status(thm)],[4056,14,15,16,17,18,19,20,21]),
[iquote('0:SSi:4056.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0')] ).
cnf(10860,plain,
( ~ ssList(u)
| ~ ssList(cons(v,nil))
| ~ ssList(u)
| equal(app(nil,cons(v,u)),cons(v,u)) ),
inference(spr,[status(thm),theory(equality)],[700,4057]),
[iquote('1:SpR:700.1,4057.2')] ).
cnf(10908,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| equal(app(nil,cons(u,v)),cons(u,v)) ),
inference(obv,[status(thm),theory(equality)],[10860]),
[iquote('1:Obv:10860.0')] ).
cnf(14274,plain,
( ~ ssList(u)
| equal(app(nil,cons(v,u)),cons(v,u)) ),
inference(ssi,[status(thm)],[10908,694,14,15,16,17,18,19,20,21,581,580,579,578,577,576,575,1780]),
[iquote('1:SSi:10908.0,694.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,581.0,580.0,579.0,578.0,577.0,576.0,575.0,1780.1')] ).
cnf(15247,plain,
( ~ ssList(app(u,cons(v,nil)))
| ~ ssList(u)
| ~ ssList(nil)
| ~ equal(app(u,cons(v,nil)),sk1)
| ~ equal(app(app(nil,cons(v,nil)),u),sk2) ),
inference(spl,[status(thm),theory(equality)],[86,769]),
[iquote('1:SpL:86.1,769.2')] ).
cnf(15256,plain,
( ~ ssList(app(u,cons(v,nil)))
| ~ ssList(u)
| ~ ssList(nil)
| ~ equal(app(u,cons(v,nil)),sk1)
| ~ equal(app(cons(v,nil),u),sk2) ),
inference(rew,[status(thm),theory(equality)],[14274,15247]),
[iquote('1:Rew:14274.1,15247.4')] ).
cnf(15257,plain,
( ~ ssList(app(u,cons(v,nil)))
| ~ ssList(u)
| ~ ssList(nil)
| ~ equal(app(u,cons(v,nil)),sk1)
| ~ equal(cons(v,u),sk2) ),
inference(rew,[status(thm),theory(equality)],[87,15256,766]),
[iquote('1:Rew:87.1,15256.4,766.2,15256.4')] ).
cnf(15258,plain,
( ~ ssList(u)
| ~ equal(app(u,cons(v,nil)),sk1)
| ~ equal(cons(v,u),sk2) ),
inference(ssi,[status(thm)],[15257,14,15,16,17,18,19,20,21,98,694,581,580,579,578,577,576,575,1780]),
[iquote('1:SSi:15257.2,15257.0,14.0,15.0,16.0,17.0,18.0,19.0,20.0,21.0,98.0,694.0,14.0,15.0,16.0,17.0,18.0,19.0,20.1,21.2,581.0,580.0,579.0,578.0,577.0,576.0,575.0,1780.0')] ).
cnf(23966,plain,
( ~ ssList(sk6)
| ~ equal(sk1,sk1)
| ~ equal(cons(sk5,sk6),sk2) ),
inference(spl,[status(thm),theory(equality)],[207,15258]),
[iquote('1:SpL:207.0,15258.1')] ).
cnf(24727,plain,
( ~ ssList(sk6)
| ~ equal(cons(sk5,sk6),sk2) ),
inference(obv,[status(thm),theory(equality)],[23966]),
[iquote('1:Obv:23966.1')] ).
cnf(24728,plain,
( ~ ssList(sk6)
| ~ equal(sk2,sk2) ),
inference(rew,[status(thm),theory(equality)],[1901,24727]),
[iquote('1:Rew:1901.0,24727.1')] ).
cnf(24729,plain,
~ ssList(sk6),
inference(obv,[status(thm),theory(equality)],[24728]),
[iquote('1:Obv:24728.1')] ).
cnf(24730,plain,
$false,
inference(ssi,[status(thm)],[24729,202]),
[iquote('1:SSi:24729.0,202.0')] ).
cnf(25137,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[85]),
[iquote('1:Spt:24730.0,85.0,85.2')] ).
cnf(25351,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)],[192,25137]),
[iquote('1:MRR:192.1,25137.1')] ).
cnf(44650,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)],[170,98]),
[iquote('0:SpR:170.3,98.2')] ).
cnf(44696,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[44650]),
[iquote('0:Obv:44650.0')] ).
cnf(44697,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[44696,99]),
[iquote('0:SSi:44696.2,99.2')] ).
cnf(45958,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)],[25351]),
[iquote('1:EqR:25351.5')] ).
cnf(45983,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[45958,98,99]),
[iquote('1:SSi:45958.0,98.2,98.2,99.2,99.2')] ).
cnf(45984,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[44697,45983]),
[iquote('1:MRR:44697.3,45983.1')] ).
cnf(45990,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[45984]),
[iquote('1:Con:45984.2')] ).
cnf(45991,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[525,45990]),
[iquote('1:MRR:525.1,45990.0')] ).
cnf(45994,plain,
$false,
inference(unc,[status(thm)],[45991,60]),
[iquote('1:UnC:45991.0,60.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC419-1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 12 18:40:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 41.32/41.53
% 41.32/41.53 SPASS V 3.9
% 41.32/41.53 SPASS beiseite: Proof found.
% 41.32/41.53 % SZS status Theorem
% 41.32/41.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.32/41.53 SPASS derived 28986 clauses, backtracked 9841 clauses, performed 91 splits and kept 19083 clauses.
% 41.32/41.53 SPASS allocated 110061 KBytes.
% 41.32/41.53 SPASS spent 0:0:31.51 on the problem.
% 41.32/41.53 0:00:00.04 for the input.
% 41.32/41.53 0:00:00.00 for the FLOTTER CNF translation.
% 41.32/41.53 0:00:00.36 for inferences.
% 41.32/41.53 0:00:01.75 for the backtracking.
% 41.32/41.53 0:0:28.95 for the reduction.
% 41.32/41.53
% 41.32/41.53
% 41.32/41.53 Here is a proof with depth 2, length 84 :
% 41.32/41.53 % SZS output start Refutation
% See solution above
% 41.32/41.54 Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_8 co1_11 co1_12 co1_13 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause47 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause85 clause86 clause116 clause120 clause149 clause157 clause179
% 41.32/41.54
%------------------------------------------------------------------------------