TSTP Solution File: SWC002-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC002-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 22:01:00 EDT 2022
% Result : Unsatisfiable 22.46s 22.69s
% Output : Refutation 22.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of clauses : 72 ( 17 unt; 4 nHn; 72 RR)
% Number of literals : 240 ( 0 equ; 180 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
ssList(sk2),
file('SWC002-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC002-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC002-1.p',unknown),
[] ).
cnf(7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('SWC002-1.p',unknown),
[] ).
cnf(14,axiom,
( ssList(sk7)
| neq(sk2,nil) ),
file('SWC002-1.p',unknown),
[] ).
cnf(15,axiom,
( ssList(sk8)
| neq(sk2,nil) ),
file('SWC002-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(v,w),sk1)
| ~ neq(sk4,nil)
| memberP(sk2,sk5(w,v,u)) ),
file('SWC002-1.p',unknown),
[] ).
cnf(21,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(v,w),sk1)
| ~ neq(sk4,nil)
| geq(sk5(w,v,u),u) ),
file('SWC002-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(v,w),sk1)
| ~ equal(sk5(w,v,u),u)
| ~ neq(sk4,nil) ),
file('SWC002-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('SWC002-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ neq(sk4,nil)
| ssList(sk8) ),
file('SWC002-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ neq(sk4,nil)
| equal(app(app(sk7,cons(sk6,nil)),sk8),sk4) ),
file('SWC002-1.p',unknown),
[] ).
cnf(27,axiom,
( ~ neq(sk4,nil)
| equal(app(sk7,sk8),sk3) ),
file('SWC002-1.p',unknown),
[] ).
cnf(28,axiom,
( ~ ssItem(u)
| ~ memberP(sk4,u)
| ~ geq(u,sk6)
| ~ neq(sk4,nil)
| equal(sk6,u) ),
file('SWC002-1.p',unknown),
[] ).
cnf(40,axiom,
ssItem(skaf83(u)),
file('SWC002-1.p',unknown),
[] ).
cnf(100,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC002-1.p',unknown),
[] ).
cnf(113,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC002-1.p',unknown),
[] ).
cnf(114,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC002-1.p',unknown),
[] ).
cnf(185,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC002-1.p',unknown),
[] ).
cnf(207,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('SWC002-1.p',unknown),
[] ).
cnf(216,plain,
( ~ neq(sk2,nil)
| ssList(sk8) ),
inference(rew,[status(thm),theory(equality)],[5,25]),
[iquote('0:Rew:5.0,25.0')] ).
cnf(217,plain,
ssList(sk8),
inference(mrr,[status(thm)],[216,15]),
[iquote('0:MRR:216.0,15.1')] ).
cnf(218,plain,
( ~ neq(sk2,nil)
| ssList(sk7) ),
inference(rew,[status(thm),theory(equality)],[5,24]),
[iquote('0:Rew:5.0,24.0')] ).
cnf(219,plain,
ssList(sk7),
inference(mrr,[status(thm)],[218,14]),
[iquote('0:MRR:218.0,14.1')] ).
cnf(222,plain,
neq(sk2,nil),
inference(obv,[status(thm),theory(equality)],[7]),
[iquote('0:Obv:7.0')] ).
cnf(223,plain,
( ~ neq(sk2,nil)
| equal(app(sk7,sk8),sk1) ),
inference(rew,[status(thm),theory(equality)],[6,27,5]),
[iquote('0:Rew:6.0,27.1,5.0,27.0')] ).
cnf(224,plain,
equal(app(sk7,sk8),sk1),
inference(mrr,[status(thm)],[223,222]),
[iquote('0:MRR:223.0,222.0')] ).
cnf(225,plain,
( ~ neq(sk2,nil)
| equal(app(app(sk7,cons(sk6,nil)),sk8),sk2) ),
inference(rew,[status(thm),theory(equality)],[5,26]),
[iquote('0:Rew:5.0,26.1,5.0,26.0')] ).
cnf(226,plain,
equal(app(app(sk7,cons(sk6,nil)),sk8),sk2),
inference(mrr,[status(thm)],[225,222]),
[iquote('0:MRR:225.0,222.0')] ).
cnf(227,plain,
( ~ ssItem(u)
| ~ memberP(sk2,u)
| ~ geq(u,sk6)
| ~ neq(sk2,nil)
| equal(sk6,u) ),
inference(rew,[status(thm),theory(equality)],[5,28]),
[iquote('0:Rew:5.0,28.3,5.0,28.1')] ).
cnf(228,plain,
( ~ ssItem(u)
| ~ geq(u,sk6)
| ~ memberP(sk2,u)
| equal(sk6,u) ),
inference(mrr,[status(thm)],[227,222]),
[iquote('0:MRR:227.3,222.0')] ).
cnf(235,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(v,w),sk1)
| ~ neq(sk2,nil)
| memberP(sk2,sk5(w,v,u)) ),
inference(rew,[status(thm),theory(equality)],[5,20]),
[iquote('0:Rew:5.0,20.5')] ).
cnf(236,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(v,u),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2)
| memberP(sk2,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[235,222]),
[iquote('0:MRR:235.5,222.0')] ).
cnf(237,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(v,w),sk1)
| ~ neq(sk2,nil)
| geq(sk5(w,v,u),u) ),
inference(rew,[status(thm),theory(equality)],[5,21]),
[iquote('0:Rew:5.0,21.5')] ).
cnf(238,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(v,u),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2)
| geq(sk5(u,v,w),w) ),
inference(mrr,[status(thm)],[237,222]),
[iquote('0:MRR:237.5,222.0')] ).
cnf(239,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(v,w),sk1)
| ~ equal(sk5(w,v,u),u)
| ~ neq(sk2,nil) ),
inference(rew,[status(thm),theory(equality)],[5,22]),
[iquote('0:Rew:5.0,22.6')] ).
cnf(240,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(v,u),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2)
| ~ equal(sk5(u,v,w),w) ),
inference(mrr,[status(thm)],[239,222]),
[iquote('0:MRR:239.6,222.0')] ).
cnf(382,plain,
( ~ ssItem(u)
| ssList(cons(u,sk2)) ),
inference(res,[status(thm),theory(equality)],[2,114]),
[iquote('0:Res:2.0,114.1')] ).
cnf(603,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[100]),
[iquote('1:Spt:100.1')] ).
cnf(649,plain,
( ~ geq(u,sk6)
| ~ memberP(sk2,u)
| equal(sk6,u) ),
inference(mrr,[status(thm)],[228,603]),
[iquote('1:MRR:228.0,603.0')] ).
cnf(812,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,u),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2)
| geq(sk5(u,v,w),w) ),
inference(mrr,[status(thm)],[238,603]),
[iquote('1:MRR:238.2,603.0')] ).
cnf(813,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,u),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2)
| memberP(sk2,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[236,603]),
[iquote('1:MRR:236.2,603.0')] ).
cnf(814,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(v,u),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2)
| ~ equal(sk5(u,v,w),w) ),
inference(mrr,[status(thm)],[240,603]),
[iquote('1:MRR:240.2,603.0')] ).
cnf(9847,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(app(sk7,sk8),sk1)
| ~ equal(sk2,sk2)
| memberP(sk2,sk5(sk8,sk7,sk6)) ),
inference(spl,[status(thm),theory(equality)],[226,813]),
[iquote('1:SpL:226.0,813.3')] ).
cnf(9848,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(app(sk7,sk8),sk1)
| memberP(sk2,sk5(sk8,sk7,sk6)) ),
inference(obv,[status(thm),theory(equality)],[9847]),
[iquote('1:Obv:9847.3')] ).
cnf(9849,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk1,sk1)
| memberP(sk2,sk5(sk8,sk7,sk6)) ),
inference(rew,[status(thm),theory(equality)],[224,9848]),
[iquote('1:Rew:224.0,9848.2')] ).
cnf(9850,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| memberP(sk2,sk5(sk8,sk7,sk6)) ),
inference(obv,[status(thm),theory(equality)],[9849]),
[iquote('1:Obv:9849.2')] ).
cnf(9851,plain,
memberP(sk2,sk5(sk8,sk7,sk6)),
inference(ssi,[status(thm)],[9850,219,217]),
[iquote('1:SSi:9850.1,9850.0,219.0,217.0')] ).
cnf(9953,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(app(sk7,sk8),sk1)
| ~ equal(sk2,sk2)
| geq(sk5(sk8,sk7,sk6),sk6) ),
inference(spl,[status(thm),theory(equality)],[226,812]),
[iquote('1:SpL:226.0,812.3')] ).
cnf(9954,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(app(sk7,sk8),sk1)
| geq(sk5(sk8,sk7,sk6),sk6) ),
inference(obv,[status(thm),theory(equality)],[9953]),
[iquote('1:Obv:9953.3')] ).
cnf(9955,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk1,sk1)
| geq(sk5(sk8,sk7,sk6),sk6) ),
inference(rew,[status(thm),theory(equality)],[224,9954]),
[iquote('1:Rew:224.0,9954.2')] ).
cnf(9956,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| geq(sk5(sk8,sk7,sk6),sk6) ),
inference(obv,[status(thm),theory(equality)],[9955]),
[iquote('1:Obv:9955.2')] ).
cnf(9957,plain,
geq(sk5(sk8,sk7,sk6),sk6),
inference(ssi,[status(thm)],[9956,219,217]),
[iquote('1:SSi:9956.1,9956.0,219.0,217.0')] ).
cnf(10080,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(app(sk7,sk8),sk1)
| ~ equal(sk2,sk2)
| ~ equal(sk5(sk8,sk7,sk6),sk6) ),
inference(spl,[status(thm),theory(equality)],[226,814]),
[iquote('1:SpL:226.0,814.3')] ).
cnf(10081,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(app(sk7,sk8),sk1)
| ~ equal(sk5(sk8,sk7,sk6),sk6) ),
inference(obv,[status(thm),theory(equality)],[10080]),
[iquote('1:Obv:10080.3')] ).
cnf(10082,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk1,sk1)
| ~ equal(sk5(sk8,sk7,sk6),sk6) ),
inference(rew,[status(thm),theory(equality)],[224,10081]),
[iquote('1:Rew:224.0,10081.2')] ).
cnf(10083,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk5(sk8,sk7,sk6),sk6) ),
inference(obv,[status(thm),theory(equality)],[10082]),
[iquote('1:Obv:10082.2')] ).
cnf(10084,plain,
~ equal(sk5(sk8,sk7,sk6),sk6),
inference(ssi,[status(thm)],[10083,219,217]),
[iquote('1:SSi:10083.1,10083.0,219.0,217.0')] ).
cnf(10141,plain,
( ~ memberP(sk2,sk5(sk8,sk7,sk6))
| equal(sk5(sk8,sk7,sk6),sk6) ),
inference(res,[status(thm),theory(equality)],[9957,649]),
[iquote('1:Res:9957.0,649.0')] ).
cnf(10143,plain,
equal(sk5(sk8,sk7,sk6),sk6),
inference(mrr,[status(thm)],[10141,9851]),
[iquote('1:MRR:10141.0,9851.0')] ).
cnf(10144,plain,
$false,
inference(mrr,[status(thm)],[10143,10084]),
[iquote('1:MRR:10143.0,10084.0')] ).
cnf(10145,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[100]),
[iquote('1:Spt:10144.0,100.0,100.2')] ).
cnf(10183,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)],[207,10145]),
[iquote('1:MRR:207.1,10145.1')] ).
cnf(34203,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)],[185,113]),
[iquote('0:SpR:185.3,113.2')] ).
cnf(34246,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[34203]),
[iquote('0:Obv:34203.0')] ).
cnf(34247,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[34246,114]),
[iquote('0:SSi:34246.2,114.2')] ).
cnf(35763,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)],[10183]),
[iquote('1:EqR:10183.5')] ).
cnf(35795,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[35763,113,114]),
[iquote('1:SSi:35763.0,113.2,113.2,114.2,114.2')] ).
cnf(35796,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[34247,35795]),
[iquote('1:MRR:34247.3,35795.1')] ).
cnf(35799,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[35796]),
[iquote('1:Con:35796.2')] ).
cnf(35801,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[382,35799]),
[iquote('1:MRR:382.1,35799.0')] ).
cnf(35803,plain,
$false,
inference(unc,[status(thm)],[35801,40]),
[iquote('1:UnC:35801.0,40.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC002-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 12 16:41:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 22.46/22.69
% 22.46/22.69 SPASS V 3.9
% 22.46/22.69 SPASS beiseite: Proof found.
% 22.46/22.69 % SZS status Theorem
% 22.46/22.69 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.46/22.69 SPASS derived 24302 clauses, backtracked 9995 clauses, performed 118 splits and kept 20417 clauses.
% 22.46/22.69 SPASS allocated 100749 KBytes.
% 22.46/22.69 SPASS spent 0:0:16.97 on the problem.
% 22.46/22.69 0:00:00.04 for the input.
% 22.46/22.69 0:00:00.00 for the FLOTTER CNF translation.
% 22.46/22.69 0:00:00.19 for inferences.
% 22.46/22.69 0:00:00.60 for the backtracking.
% 22.46/22.69 0:0:15.83 for the reduction.
% 22.46/22.69
% 22.46/22.69
% 22.46/22.69 Here is a proof with depth 2, length 72 :
% 22.46/22.69 % SZS output start Refutation
% See solution above
% 22.46/22.69 Formulae used in the proof : co1_2 co1_5 co1_6 co1_7 co1_14 co1_15 co1_20 co1_21 co1_22 co1_24 co1_25 co1_26 co1_27 co1_28 clause12 clause72 clause85 clause86 clause157 clause179
% 22.46/22.69
%------------------------------------------------------------------------------