TSTP Solution File: SWC417-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC417-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 22:03:56 EDT 2022
% Result : Unsatisfiable 50.53s 50.74s
% Output : Refutation 50.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 35
% Syntax : Number of clauses : 88 ( 30 unt; 3 nHn; 88 RR)
% Number of literals : 215 ( 0 equ; 143 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('SWC417-1.p',unknown),
[] ).
cnf(5,axiom,
equal(sk4,sk2),
file('SWC417-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC417-1.p',unknown),
[] ).
cnf(7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('SWC417-1.p',unknown),
[] ).
cnf(11,axiom,
( ssList(sk6)
| neq(sk2,nil) ),
file('SWC417-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(app(w,cons(u,nil)),v),sk1)
| ~ neq(sk4,nil) ),
file('SWC417-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('SWC417-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ neq(sk4,nil)
| equal(app(cons(sk5,nil),sk6),sk4) ),
file('SWC417-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ neq(sk4,nil)
| equal(app(sk6,cons(sk5,nil)),sk3) ),
file('SWC417-1.p',unknown),
[] ).
cnf(19,axiom,
equalelemsP(nil),
file('SWC417-1.p',unknown),
[] ).
cnf(20,axiom,
duplicatefreeP(nil),
file('SWC417-1.p',unknown),
[] ).
cnf(21,axiom,
strictorderedP(nil),
file('SWC417-1.p',unknown),
[] ).
cnf(22,axiom,
totalorderedP(nil),
file('SWC417-1.p',unknown),
[] ).
cnf(23,axiom,
strictorderP(nil),
file('SWC417-1.p',unknown),
[] ).
cnf(24,axiom,
totalorderP(nil),
file('SWC417-1.p',unknown),
[] ).
cnf(25,axiom,
cyclefreeP(nil),
file('SWC417-1.p',unknown),
[] ).
cnf(26,axiom,
ssList(nil),
file('SWC417-1.p',unknown),
[] ).
cnf(65,axiom,
ssItem(skaf44(u)),
file('SWC417-1.p',unknown),
[] ).
cnf(82,axiom,
( ~ ssItem(u)
| equalelemsP(cons(u,nil)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ ssItem(u)
| duplicatefreeP(cons(u,nil)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(84,axiom,
( ~ ssItem(u)
| strictorderedP(cons(u,nil)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(85,axiom,
( ~ ssItem(u)
| totalorderedP(cons(u,nil)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(86,axiom,
( ~ ssItem(u)
| strictorderP(cons(u,nil)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(87,axiom,
( ~ ssItem(u)
| totalorderP(cons(u,nil)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(88,axiom,
( ~ ssItem(u)
| cyclefreeP(cons(u,nil)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(90,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC417-1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| equal(app(u,nil),u) ),
file('SWC417-1.p',unknown),
[] ).
cnf(92,axiom,
( ~ ssList(u)
| equal(app(nil,u),u) ),
file('SWC417-1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(104,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(134,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
file('SWC417-1.p',unknown),
[] ).
cnf(138,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| equal(app(cons(v,nil),u),cons(v,u)) ),
file('SWC417-1.p',unknown),
[] ).
cnf(167,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| equal(app(app(u,v),w),app(u,app(v,w))) ),
file('SWC417-1.p',unknown),
[] ).
cnf(175,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC417-1.p',unknown),
[] ).
cnf(197,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('SWC417-1.p',unknown),
[] ).
cnf(206,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(rew,[status(thm),theory(equality)],[5,16]),
[iquote('0:Rew:5.0,16.0')] ).
cnf(207,plain,
ssList(sk6),
inference(mrr,[status(thm)],[206,11]),
[iquote('0:MRR:206.0,11.1')] ).
cnf(210,plain,
neq(sk2,nil),
inference(obv,[status(thm),theory(equality)],[7]),
[iquote('0:Obv:7.0')] ).
cnf(211,plain,
( ~ neq(sk2,nil)
| equal(app(sk6,cons(sk5,nil)),sk1) ),
inference(rew,[status(thm),theory(equality)],[6,18,5]),
[iquote('0:Rew:6.0,18.1,5.0,18.0')] ).
cnf(212,plain,
equal(app(sk6,cons(sk5,nil)),sk1),
inference(mrr,[status(thm)],[211,210]),
[iquote('0:MRR:211.0,210.0')] ).
cnf(213,plain,
( ~ neq(sk2,nil)
| equal(app(cons(sk5,nil),sk6),sk2) ),
inference(rew,[status(thm),theory(equality)],[5,17]),
[iquote('0:Rew:5.0,17.1,5.0,17.0')] ).
cnf(214,plain,
equal(app(cons(sk5,nil),sk6),sk2),
inference(mrr,[status(thm)],[213,210]),
[iquote('0:MRR:213.0,210.0')] ).
cnf(219,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ equal(app(app(v,cons(u,nil)),w),sk2)
| ~ equal(app(app(w,cons(u,nil)),v),sk1)
| ~ neq(sk2,nil) ),
inference(rew,[status(thm),theory(equality)],[5,14]),
[iquote('0:Rew:5.0,14.5')] ).
cnf(220,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(u,cons(w,nil)),v),sk1)
| ~ equal(app(app(v,cons(w,nil)),u),sk2) ),
inference(mrr,[status(thm)],[219,210]),
[iquote('0:MRR:219.5,210.0')] ).
cnf(532,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,104]),
[iquote('0:Res:1.0,104.1')] ).
cnf(571,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[90]),
[iquote('1:Spt:90.1')] ).
cnf(577,plain,
cyclefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[88,571]),
[iquote('1:MRR:88.0,571.0')] ).
cnf(578,plain,
totalorderP(cons(u,nil)),
inference(mrr,[status(thm)],[87,571]),
[iquote('1:MRR:87.0,571.0')] ).
cnf(579,plain,
strictorderP(cons(u,nil)),
inference(mrr,[status(thm)],[86,571]),
[iquote('1:MRR:86.0,571.0')] ).
cnf(580,plain,
totalorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[85,571]),
[iquote('1:MRR:85.0,571.0')] ).
cnf(581,plain,
strictorderedP(cons(u,nil)),
inference(mrr,[status(thm)],[84,571]),
[iquote('1:MRR:84.0,571.0')] ).
cnf(582,plain,
duplicatefreeP(cons(u,nil)),
inference(mrr,[status(thm)],[83,571]),
[iquote('1:MRR:83.0,571.0')] ).
cnf(583,plain,
equalelemsP(cons(u,nil)),
inference(mrr,[status(thm)],[82,571]),
[iquote('1:MRR:82.0,571.0')] ).
cnf(696,plain,
( ~ ssList(u)
| ssList(cons(v,u)) ),
inference(mrr,[status(thm)],[104,571]),
[iquote('1:MRR:104.1,571.0')] ).
cnf(701,plain,
( ~ ssList(u)
| ~ equal(cons(v,nil),u)
| singletonP(u) ),
inference(mrr,[status(thm)],[134,571]),
[iquote('1:MRR:134.1,571.0')] ).
cnf(702,plain,
( ~ ssList(u)
| equal(app(cons(v,nil),u),cons(v,u)) ),
inference(mrr,[status(thm)],[138,571]),
[iquote('1:MRR:138.1,571.0')] ).
cnf(768,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
inference(mrr,[status(thm)],[175,571]),
[iquote('1:MRR:175.2,571.0')] ).
cnf(771,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)],[220,571]),
[iquote('1:MRR:220.2,571.0')] ).
cnf(3078,plain,
( ~ ssList(cons(u,nil))
| singletonP(cons(u,nil)) ),
inference(eqr,[status(thm),theory(equality)],[701]),
[iquote('1:EqR:701.1')] ).
cnf(3079,plain,
singletonP(cons(u,nil)),
inference(ssi,[status(thm)],[3078,696,26,25,24,23,22,21,20,19,577,578,579,580,581,582,583]),
[iquote('1:SSi:3078.0,696.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,577.0,578.0,579.0,580.0,581.0,582.0,583.1')] ).
cnf(3179,plain,
( ~ ssList(sk6)
| equal(cons(sk5,sk6),sk2) ),
inference(spr,[status(thm),theory(equality)],[702,214]),
[iquote('1:SpR:702.1,214.0')] ).
cnf(3190,plain,
equal(cons(sk5,sk6),sk2),
inference(ssi,[status(thm)],[3179,207]),
[iquote('1:SSi:3179.0,207.0')] ).
cnf(5348,plain,
( ~ ssList(u)
| ~ ssList(nil)
| ~ ssList(u)
| ~ ssList(v)
| equal(app(nil,app(u,v)),app(u,v)) ),
inference(spr,[status(thm),theory(equality)],[92,167]),
[iquote('0:SpR:92.1,167.3')] ).
cnf(5371,plain,
( ~ ssList(nil)
| ~ ssList(u)
| ~ ssList(v)
| equal(app(nil,app(u,v)),app(u,v)) ),
inference(obv,[status(thm),theory(equality)],[5348]),
[iquote('0:Obv:5348.0')] ).
cnf(5372,plain,
( ~ ssList(u)
| ~ ssList(v)
| equal(app(nil,app(u,v)),app(u,v)) ),
inference(ssi,[status(thm)],[5371,26,25,24,23,22,21,20,19]),
[iquote('0:SSi:5371.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0')] ).
cnf(12178,plain,
( ~ ssList(u)
| ~ ssList(cons(v,nil))
| ~ ssList(u)
| equal(app(nil,cons(v,u)),cons(v,u)) ),
inference(spr,[status(thm),theory(equality)],[702,5372]),
[iquote('1:SpR:702.1,5372.2')] ).
cnf(12223,plain,
( ~ ssList(cons(u,nil))
| ~ ssList(v)
| equal(app(nil,cons(u,v)),cons(u,v)) ),
inference(obv,[status(thm),theory(equality)],[12178]),
[iquote('1:Obv:12178.0')] ).
cnf(15590,plain,
( ~ ssList(u)
| equal(app(nil,cons(v,u)),cons(v,u)) ),
inference(ssi,[status(thm)],[12223,696,26,25,24,23,22,21,20,19,577,578,579,580,581,582,583,3079]),
[iquote('1:SSi:12223.0,696.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,577.0,578.0,579.0,580.0,581.0,582.0,583.0,3079.1')] ).
cnf(16560,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)],[91,771]),
[iquote('1:SpL:91.1,771.2')] ).
cnf(16569,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)],[15590,16560]),
[iquote('1:Rew:15590.1,16560.4')] ).
cnf(16570,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)],[92,16569,768]),
[iquote('1:Rew:92.1,16569.4,768.2,16569.4')] ).
cnf(16571,plain,
( ~ ssList(u)
| ~ equal(app(u,cons(v,nil)),sk1)
| ~ equal(cons(v,u),sk2) ),
inference(ssi,[status(thm)],[16570,26,25,24,23,22,21,20,19,103,696,577,578,579,580,581,582,583,3079]),
[iquote('1:SSi:16570.2,16570.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0,103.0,696.0,26.0,25.0,24.0,23.0,22.0,21.0,20.1,19.2,577.0,578.0,579.0,580.0,581.0,582.0,583.0,3079.0')] ).
cnf(23710,plain,
( ~ ssList(sk6)
| ~ equal(sk1,sk1)
| ~ equal(cons(sk5,sk6),sk2) ),
inference(spl,[status(thm),theory(equality)],[212,16571]),
[iquote('1:SpL:212.0,16571.1')] ).
cnf(24479,plain,
( ~ ssList(sk6)
| ~ equal(cons(sk5,sk6),sk2) ),
inference(obv,[status(thm),theory(equality)],[23710]),
[iquote('1:Obv:23710.1')] ).
cnf(24480,plain,
( ~ ssList(sk6)
| ~ equal(sk2,sk2) ),
inference(rew,[status(thm),theory(equality)],[3190,24479]),
[iquote('1:Rew:3190.0,24479.1')] ).
cnf(24481,plain,
~ ssList(sk6),
inference(obv,[status(thm),theory(equality)],[24480]),
[iquote('1:Obv:24480.1')] ).
cnf(24482,plain,
$false,
inference(ssi,[status(thm)],[24481,207]),
[iquote('1:SSi:24481.0,207.0')] ).
cnf(24883,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[90]),
[iquote('1:Spt:24482.0,90.0,90.2')] ).
cnf(25087,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)],[197,24883]),
[iquote('1:MRR:197.1,24883.1')] ).
cnf(49970,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)],[175,103]),
[iquote('0:SpR:175.3,103.2')] ).
cnf(50015,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[49970]),
[iquote('0:Obv:49970.0')] ).
cnf(50016,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[50015,104]),
[iquote('0:SSi:50015.2,104.2')] ).
cnf(51484,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)],[25087]),
[iquote('1:EqR:25087.5')] ).
cnf(51509,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[51484,103,104]),
[iquote('1:SSi:51484.0,103.2,103.2,104.2,104.2')] ).
cnf(51510,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[50016,51509]),
[iquote('1:MRR:50016.3,51509.1')] ).
cnf(51516,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[51510]),
[iquote('1:Con:51510.2')] ).
cnf(51517,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[532,51516]),
[iquote('1:MRR:532.1,51516.0')] ).
cnf(51520,plain,
$false,
inference(unc,[status(thm)],[51517,65]),
[iquote('1:UnC:51517.0,65.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC417-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 18:43:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 50.53/50.74
% 50.53/50.74 SPASS V 3.9
% 50.53/50.74 SPASS beiseite: Proof found.
% 50.53/50.74 % SZS status Theorem
% 50.53/50.74 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.53/50.74 SPASS derived 33125 clauses, backtracked 13381 clauses, performed 116 splits and kept 25784 clauses.
% 50.53/50.74 SPASS allocated 113070 KBytes.
% 50.53/50.74 SPASS spent 0:0:38.44 on the problem.
% 50.53/50.74 0:00:00.04 for the input.
% 50.53/50.74 0:00:00.00 for the FLOTTER CNF translation.
% 50.53/50.74 0:00:00.40 for inferences.
% 50.53/50.74 0:00:02.32 for the backtracking.
% 50.53/50.74 0:0:35.23 for the reduction.
% 50.53/50.74
% 50.53/50.74
% 50.53/50.74 Here is a proof with depth 2, length 88 :
% 50.53/50.74 % SZS output start Refutation
% See solution above
% 50.53/50.74 Formulae used in the proof : co1_1 co1_5 co1_6 co1_7 co1_11 co1_14 co1_16 co1_17 co1_18 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
% 50.53/50.74
%------------------------------------------------------------------------------