TSTP Solution File: SWC046-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC046-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 22:01:20 EDT 2022
% Result : Unsatisfiable 1.82s 2.06s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of clauses : 81 ( 34 unt; 5 nHn; 81 RR)
% Number of literals : 155 ( 0 equ; 80 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC046-1.p',unknown),
[] ).
cnf(4,axiom,
ssList(sk4),
file('SWC046-1.p',unknown),
[] ).
cnf(5,axiom,
equal(nil,sk2),
file('SWC046-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk2,sk4),
file('SWC046-1.p',unknown),
[] ).
cnf(7,axiom,
equal(sk3,sk1),
file('SWC046-1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(nil,sk1),
file('SWC046-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ ssItem(u)
| ~ memberP(sk3,u)
| memberP(sk4,u) ),
file('SWC046-1.p',unknown),
[] ).
cnf(24,axiom,
ssItem(skaf83(u)),
file('SWC046-1.p',unknown),
[] ).
cnf(25,axiom,
ssList(skaf82(u)),
file('SWC046-1.p',unknown),
[] ).
cnf(76,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC046-1.p',unknown),
[] ).
cnf(77,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC046-1.p',unknown),
[] ).
cnf(78,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC046-1.p',unknown),
[] ).
cnf(79,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC046-1.p',unknown),
[] ).
cnf(80,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC046-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC046-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC046-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| ~ memberP(nil,u) ),
file('SWC046-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC046-1.p',unknown),
[] ).
cnf(98,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC046-1.p',unknown),
[] ).
cnf(109,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(hd(cons(v,u)),v) ),
file('SWC046-1.p',unknown),
[] ).
cnf(113,axiom,
( ~ singletonP(u)
| ~ ssList(u)
| equal(cons(skaf44(u),nil),u) ),
file('SWC046-1.p',unknown),
[] ).
cnf(121,axiom,
( ~ ssList(u)
| equal(cons(skaf83(u),skaf82(u)),u)
| equal(nil,u) ),
file('SWC046-1.p',unknown),
[] ).
cnf(128,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ equal(cons(u,nil),v)
| singletonP(v) ),
file('SWC046-1.p',unknown),
[] ).
cnf(150,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ ssList(w)
| ~ equal(u,v)
| memberP(cons(v,w),u) ),
file('SWC046-1.p',unknown),
[] ).
cnf(200,plain,
equal(nil,sk4),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(210,plain,
~ equal(sk4,sk1),
inference(rew,[status(thm),theory(equality)],[200,8]),
[iquote('0:Rew:200.0,8.0')] ).
cnf(214,plain,
( ~ ssItem(u)
| ~ memberP(sk4,u) ),
inference(rew,[status(thm),theory(equality)],[200,83]),
[iquote('0:Rew:200.0,83.1')] ).
cnf(215,plain,
( ~ ssItem(u)
| cyclefreeP(cons(u,sk4)) ),
inference(rew,[status(thm),theory(equality)],[200,82]),
[iquote('0:Rew:200.0,82.1')] ).
cnf(216,plain,
( ~ ssItem(u)
| totalorderP(cons(u,sk4)) ),
inference(rew,[status(thm),theory(equality)],[200,81]),
[iquote('0:Rew:200.0,81.1')] ).
cnf(217,plain,
( ~ ssItem(u)
| strictorderP(cons(u,sk4)) ),
inference(rew,[status(thm),theory(equality)],[200,80]),
[iquote('0:Rew:200.0,80.1')] ).
cnf(218,plain,
( ~ ssItem(u)
| totalorderedP(cons(u,sk4)) ),
inference(rew,[status(thm),theory(equality)],[200,79]),
[iquote('0:Rew:200.0,79.1')] ).
cnf(219,plain,
( ~ ssItem(u)
| strictorderedP(cons(u,sk4)) ),
inference(rew,[status(thm),theory(equality)],[200,78]),
[iquote('0:Rew:200.0,78.1')] ).
cnf(220,plain,
( ~ ssItem(u)
| duplicatefreeP(cons(u,sk4)) ),
inference(rew,[status(thm),theory(equality)],[200,77]),
[iquote('0:Rew:200.0,77.1')] ).
cnf(221,plain,
( ~ ssItem(u)
| equalelemsP(cons(u,sk4)) ),
inference(rew,[status(thm),theory(equality)],[200,76]),
[iquote('0:Rew:200.0,76.1')] ).
cnf(234,plain,
( ~ ssItem(u)
| ~ memberP(sk1,u)
| memberP(sk4,u) ),
inference(rew,[status(thm),theory(equality)],[7,11]),
[iquote('0:Rew:7.0,11.1')] ).
cnf(235,plain,
( ~ ssItem(u)
| ~ memberP(sk1,u) ),
inference(mrr,[status(thm)],[234,214]),
[iquote('0:MRR:234.2,214.1')] ).
cnf(236,plain,
( ~ ssList(u)
| ~ singletonP(u)
| equal(cons(skaf44(u),sk4),u) ),
inference(rew,[status(thm),theory(equality)],[200,113]),
[iquote('0:Rew:200.0,113.2')] ).
cnf(238,plain,
( ~ ssList(u)
| equal(sk4,u)
| equal(cons(skaf83(u),skaf82(u)),u) ),
inference(rew,[status(thm),theory(equality)],[200,121]),
[iquote('0:Rew:200.0,121.2')] ).
cnf(240,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,sk4),u)
| singletonP(u) ),
inference(rew,[status(thm),theory(equality)],[200,128]),
[iquote('0:Rew:200.0,128.2')] ).
cnf(393,plain,
( ~ ssItem(u)
| equal(hd(cons(u,sk4)),u) ),
inference(res,[status(thm),theory(equality)],[4,109]),
[iquote('0:Res:4.0,109.1')] ).
cnf(398,plain,
( ~ ssItem(u)
| ssList(cons(u,sk4)) ),
inference(res,[status(thm),theory(equality)],[4,98]),
[iquote('0:Res:4.0,98.1')] ).
cnf(490,plain,
( equal(cons(skaf83(sk1),skaf82(sk1)),sk1)
| equal(sk4,sk1) ),
inference(res,[status(thm),theory(equality)],[1,238]),
[iquote('0:Res:1.0,238.0')] ).
cnf(513,plain,
( ssItem(u)
| duplicatefreeP(sk1) ),
inference(res,[status(thm),theory(equality)],[1,84]),
[iquote('0:Res:1.0,84.0')] ).
cnf(614,plain,
equal(cons(skaf83(sk1),skaf82(sk1)),sk1),
inference(mrr,[status(thm)],[490,210]),
[iquote('0:MRR:490.1,210.0')] ).
cnf(679,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[84]),
[iquote('1:Spt:84.1')] ).
cnf(693,plain,
~ memberP(sk1,u),
inference(mrr,[status(thm)],[235,679]),
[iquote('1:MRR:235.0,679.0')] ).
cnf(699,plain,
equal(hd(cons(u,sk4)),u),
inference(mrr,[status(thm)],[393,679]),
[iquote('1:MRR:393.0,679.0')] ).
cnf(740,plain,
( ~ ssList(u)
| ~ equal(v,w)
| memberP(cons(w,u),v) ),
inference(mrr,[status(thm)],[150,679]),
[iquote('1:MRR:150.1,150.0,679.0')] ).
cnf(1202,plain,
( ~ ssList(skaf82(sk1))
| ~ equal(u,skaf83(sk1))
| memberP(sk1,u) ),
inference(spr,[status(thm),theory(equality)],[614,740]),
[iquote('1:SpR:614.0,740.2')] ).
cnf(1359,plain,
( ~ equal(u,skaf83(sk1))
| memberP(sk1,u) ),
inference(ssi,[status(thm)],[1202,25,1]),
[iquote('1:SSi:1202.0,25.0,1.0')] ).
cnf(1360,plain,
~ equal(u,skaf83(sk1)),
inference(mrr,[status(thm)],[1359,693]),
[iquote('1:MRR:1359.1,693.0')] ).
cnf(1361,plain,
$false,
inference(unc,[status(thm)],[1360,699]),
[iquote('1:UnC:1360.0,699.0')] ).
cnf(1364,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[84]),
[iquote('1:Spt:1361.0,84.0,84.2')] ).
cnf(1372,plain,
ssItem(u),
inference(spt,[spt(split,[position(s2s1)])],[513]),
[iquote('2:Spt:513.0')] ).
cnf(1375,plain,
~ memberP(sk1,u),
inference(mrr,[status(thm)],[235,1372]),
[iquote('2:MRR:235.0,1372.0')] ).
cnf(1377,plain,
equalelemsP(cons(u,sk4)),
inference(mrr,[status(thm)],[221,1372]),
[iquote('2:MRR:221.0,1372.0')] ).
cnf(1378,plain,
duplicatefreeP(cons(u,sk4)),
inference(mrr,[status(thm)],[220,1372]),
[iquote('2:MRR:220.0,1372.0')] ).
cnf(1379,plain,
strictorderedP(cons(u,sk4)),
inference(mrr,[status(thm)],[219,1372]),
[iquote('2:MRR:219.0,1372.0')] ).
cnf(1380,plain,
totalorderedP(cons(u,sk4)),
inference(mrr,[status(thm)],[218,1372]),
[iquote('2:MRR:218.0,1372.0')] ).
cnf(1381,plain,
strictorderP(cons(u,sk4)),
inference(mrr,[status(thm)],[217,1372]),
[iquote('2:MRR:217.0,1372.0')] ).
cnf(1382,plain,
totalorderP(cons(u,sk4)),
inference(mrr,[status(thm)],[216,1372]),
[iquote('2:MRR:216.0,1372.0')] ).
cnf(1383,plain,
cyclefreeP(cons(u,sk4)),
inference(mrr,[status(thm)],[215,1372]),
[iquote('2:MRR:215.0,1372.0')] ).
cnf(1385,plain,
ssList(cons(u,sk4)),
inference(mrr,[status(thm)],[398,1372]),
[iquote('2:MRR:398.0,1372.0')] ).
cnf(1388,plain,
equal(hd(cons(u,sk4)),u),
inference(mrr,[status(thm)],[393,1372]),
[iquote('2:MRR:393.0,1372.0')] ).
cnf(1434,plain,
( ~ ssList(u)
| ~ equal(v,w)
| memberP(cons(w,u),v) ),
inference(mrr,[status(thm)],[150,1372]),
[iquote('2:MRR:150.1,150.0,1372.0')] ).
cnf(1476,plain,
( ~ ssList(u)
| ~ equal(cons(v,sk4),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[240,1372]),
[iquote('2:MRR:240.1,1372.0')] ).
cnf(1572,plain,
( ~ ssList(u)
| ~ singletonP(u)
| equal(hd(u),skaf44(u)) ),
inference(spr,[status(thm),theory(equality)],[236,1388]),
[iquote('2:SpR:236.2,1388.0')] ).
cnf(1751,plain,
( ~ ssList(cons(u,sk4))
| singletonP(cons(u,sk4)) ),
inference(eqr,[status(thm),theory(equality)],[1476]),
[iquote('2:EqR:1476.1')] ).
cnf(1753,plain,
singletonP(cons(u,sk4)),
inference(ssi,[status(thm)],[1751,1377,1378,1379,1380,1381,1382,1383,1385]),
[iquote('2:SSi:1751.0,1377.0,1378.0,1379.0,1380.0,1381.0,1382.0,1383.0,1385.0')] ).
cnf(1792,plain,
( ~ ssList(cons(u,sk4))
| ~ singletonP(cons(u,sk4))
| equal(skaf44(cons(u,sk4)),u) ),
inference(spr,[status(thm),theory(equality)],[1572,1388]),
[iquote('2:SpR:1572.2,1388.0')] ).
cnf(1800,plain,
equal(skaf44(cons(u,sk4)),u),
inference(ssi,[status(thm)],[1792,1377,1378,1379,1380,1381,1382,1383,1385,1753]),
[iquote('2:SSi:1792.1,1792.0,1377.0,1378.0,1379.0,1380.0,1381.0,1382.0,1383.0,1385.0,1753.0,1377.0,1378.0,1379.0,1380.0,1381.0,1382.0,1383.0,1385.0,1753.0')] ).
cnf(1878,plain,
( ~ ssList(skaf82(sk1))
| ~ equal(u,skaf83(sk1))
| memberP(sk1,u) ),
inference(spr,[status(thm),theory(equality)],[614,1434]),
[iquote('2:SpR:614.0,1434.2')] ).
cnf(2006,plain,
( ~ equal(u,skaf83(sk1))
| memberP(sk1,u) ),
inference(ssi,[status(thm)],[1878,25,1]),
[iquote('2:SSi:1878.0,25.0,1.0')] ).
cnf(2007,plain,
~ equal(u,skaf83(sk1)),
inference(mrr,[status(thm)],[2006,1375]),
[iquote('2:MRR:2006.1,1375.0')] ).
cnf(2008,plain,
$false,
inference(unc,[status(thm)],[2007,1800]),
[iquote('2:UnC:2007.0,1800.0')] ).
cnf(2011,plain,
duplicatefreeP(sk1),
inference(spt,[spt(split,[position(s2s2)])],[513]),
[iquote('2:Spt:2008.0,513.1')] ).
cnf(4199,plain,
( ~ ssItem(u)
| ~ ssItem(skaf83(sk1))
| ~ ssList(skaf82(sk1))
| ~ equal(u,skaf83(sk1))
| memberP(sk1,u) ),
inference(spr,[status(thm),theory(equality)],[614,150]),
[iquote('0:SpR:614.0,150.4')] ).
cnf(5782,plain,
( ~ ssItem(u)
| ~ equal(u,skaf83(sk1))
| memberP(sk1,u) ),
inference(ssi,[status(thm)],[4199,25,1,2011,24]),
[iquote('2:SSi:4199.2,4199.1,25.0,1.0,2011.0,24.0,1.0,2011.0')] ).
cnf(5783,plain,
( ~ ssItem(u)
| ~ equal(u,skaf83(sk1)) ),
inference(mrr,[status(thm)],[5782,235]),
[iquote('2:MRR:5782.2,235.1')] ).
cnf(5981,plain,
~ ssItem(skaf83(sk1)),
inference(eqr,[status(thm),theory(equality)],[5783]),
[iquote('2:EqR:5783.1')] ).
cnf(6015,plain,
$false,
inference(ssi,[status(thm)],[5981,24,1,2011]),
[iquote('2:SSi:5981.0,24.0,1.0,2011.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC046-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 11 21:52:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.82/2.06
% 1.82/2.06 SPASS V 3.9
% 1.82/2.06 SPASS beiseite: Proof found.
% 1.82/2.06 % SZS status Theorem
% 1.82/2.06 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.82/2.06 SPASS derived 3701 clauses, backtracked 1364 clauses, performed 31 splits and kept 3045 clauses.
% 1.82/2.06 SPASS allocated 80794 KBytes.
% 1.82/2.06 SPASS spent 0:00:01.64 on the problem.
% 1.82/2.06 0:00:00.04 for the input.
% 1.82/2.06 0:00:00.00 for the FLOTTER CNF translation.
% 1.82/2.06 0:00:00.04 for inferences.
% 1.82/2.06 0:00:00.03 for the backtracking.
% 1.82/2.06 0:00:01.34 for the reduction.
% 1.82/2.06
% 1.82/2.06
% 1.82/2.06 Here is a proof with depth 3, length 81 :
% 1.82/2.06 % SZS output start Refutation
% See solution above
% 1.82/2.06 Formulae used in the proof : co1_1 co1_4 co1_5 co1_6 co1_7 co1_8 co1_11 clause12 clause13 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause86 clause97 clause101 clause109 clause116 clause138
% 1.82/2.06
%------------------------------------------------------------------------------