TSTP Solution File: SWC241-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC241-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 22:02:44 EDT 2022
% Result : Unsatisfiable 25.36s 25.54s
% Output : Refutation 25.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of clauses : 45 ( 14 unt; 7 nHn; 45 RR)
% Number of literals : 123 ( 0 equ; 85 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
ssList(sk1),
file('SWC241-1.p',unknown),
[] ).
cnf(6,axiom,
equal(sk3,sk1),
file('SWC241-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(nil,sk1),
file('SWC241-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| lt(w,sk5(u,v,w)) ),
file('SWC241-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| ~ leq(w,sk5(u,v,w))
| ~ equal(app(app(v,cons(w,nil)),u),sk1) ),
file('SWC241-1.p',unknown),
[] ).
cnf(14,axiom,
( equal(sk3,nil)
| ssList(sk7) ),
file('SWC241-1.p',unknown),
[] ).
cnf(15,axiom,
( equal(sk3,nil)
| ssList(sk8) ),
file('SWC241-1.p',unknown),
[] ).
cnf(16,axiom,
( equal(sk3,nil)
| equal(app(app(sk7,cons(sk6,nil)),sk8),sk3) ),
file('SWC241-1.p',unknown),
[] ).
cnf(64,axiom,
ssItem(skaf44(u)),
file('SWC241-1.p',unknown),
[] ).
cnf(89,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC241-1.p',unknown),
[] ).
cnf(102,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC241-1.p',unknown),
[] ).
cnf(103,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC241-1.p',unknown),
[] ).
cnf(120,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ lt(u,v)
| leq(u,v) ),
file('SWC241-1.p',unknown),
[] ).
cnf(174,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC241-1.p',unknown),
[] ).
cnf(196,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('SWC241-1.p',unknown),
[] ).
cnf(205,plain,
( equal(nil,sk1)
| ssList(sk8) ),
inference(rew,[status(thm),theory(equality)],[6,15]),
[iquote('0:Rew:6.0,15.0')] ).
cnf(206,plain,
ssList(sk8),
inference(mrr,[status(thm)],[205,7]),
[iquote('0:MRR:205.0,7.0')] ).
cnf(207,plain,
( equal(nil,sk1)
| ssList(sk7) ),
inference(rew,[status(thm),theory(equality)],[6,14]),
[iquote('0:Rew:6.0,14.0')] ).
cnf(208,plain,
ssList(sk7),
inference(mrr,[status(thm)],[207,7]),
[iquote('0:MRR:207.0,7.0')] ).
cnf(211,plain,
( equal(nil,sk1)
| equal(app(app(sk7,cons(sk6,nil)),sk8),sk1) ),
inference(rew,[status(thm),theory(equality)],[6,16]),
[iquote('0:Rew:6.0,16.1,6.0,16.0')] ).
cnf(212,plain,
equal(app(app(sk7,cons(sk6,nil)),sk8),sk1),
inference(mrr,[status(thm)],[211,7]),
[iquote('0:MRR:211.0,7.0')] ).
cnf(542,plain,
( ~ ssItem(u)
| ssList(cons(u,sk1)) ),
inference(res,[status(thm),theory(equality)],[1,103]),
[iquote('0:Res:1.0,103.1')] ).
cnf(599,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[89]),
[iquote('1:Spt:89.1')] ).
cnf(638,plain,
( ~ lt(u,v)
| leq(u,v) ),
inference(mrr,[status(thm)],[120,599]),
[iquote('1:MRR:120.1,120.0,599.0')] ).
cnf(810,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ equal(app(app(v,cons(w,nil)),u),sk1)
| lt(w,sk5(u,v,w)) ),
inference(mrr,[status(thm)],[11,599]),
[iquote('1:MRR:11.2,599.0')] ).
cnf(813,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ leq(w,sk5(u,v,w))
| ~ equal(app(app(v,cons(w,nil)),u),sk1) ),
inference(mrr,[status(thm)],[12,599]),
[iquote('1:MRR:12.2,599.0')] ).
cnf(9099,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ equal(sk1,sk1)
| lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(spl,[status(thm),theory(equality)],[212,810]),
[iquote('1:SpL:212.0,810.2')] ).
cnf(9101,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(obv,[status(thm),theory(equality)],[9099]),
[iquote('1:Obv:9099.2')] ).
cnf(9102,plain,
lt(sk6,sk5(sk8,sk7,sk6)),
inference(ssi,[status(thm)],[9101,208,206]),
[iquote('1:SSi:9101.1,9101.0,208.0,206.0')] ).
cnf(9283,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ leq(sk6,sk5(sk8,sk7,sk6))
| ~ equal(sk1,sk1) ),
inference(spl,[status(thm),theory(equality)],[212,813]),
[iquote('1:SpL:212.0,813.3')] ).
cnf(9285,plain,
( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ leq(sk6,sk5(sk8,sk7,sk6)) ),
inference(obv,[status(thm),theory(equality)],[9283]),
[iquote('1:Obv:9283.3')] ).
cnf(9286,plain,
~ leq(sk6,sk5(sk8,sk7,sk6)),
inference(ssi,[status(thm)],[9285,208,206]),
[iquote('1:SSi:9285.1,9285.0,208.0,206.0')] ).
cnf(9713,plain,
~ lt(sk6,sk5(sk8,sk7,sk6)),
inference(res,[status(thm),theory(equality)],[638,9286]),
[iquote('1:Res:638.1,9286.0')] ).
cnf(9714,plain,
$false,
inference(mrr,[status(thm)],[9713,9102]),
[iquote('1:MRR:9713.0,9102.0')] ).
cnf(9715,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[89]),
[iquote('1:Spt:9714.0,89.0,89.2')] ).
cnf(9744,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)],[196,9715]),
[iquote('1:MRR:196.1,9715.1')] ).
cnf(40964,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)],[174,102]),
[iquote('0:SpR:174.3,102.2')] ).
cnf(41006,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[40964]),
[iquote('0:Obv:40964.0')] ).
cnf(41007,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[41006,103]),
[iquote('0:SSi:41006.2,103.2')] ).
cnf(43079,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)],[9744]),
[iquote('1:EqR:9744.5')] ).
cnf(43112,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[43079,102,103]),
[iquote('1:SSi:43079.0,102.2,102.2,103.2,103.2')] ).
cnf(43114,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[41007,43112]),
[iquote('1:MRR:41007.3,43112.1')] ).
cnf(43117,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[43114]),
[iquote('1:Con:43114.2')] ).
cnf(43119,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[542,43117]),
[iquote('1:MRR:542.1,43117.0')] ).
cnf(43123,plain,
$false,
inference(unc,[status(thm)],[43119,64]),
[iquote('1:UnC:43119.0,64.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC241-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jun 12 17:06:58 EDT 2022
% 0.12/0.32 % CPUTime :
% 25.36/25.54
% 25.36/25.54 SPASS V 3.9
% 25.36/25.54 SPASS beiseite: Proof found.
% 25.36/25.54 % SZS status Theorem
% 25.36/25.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.36/25.54 SPASS derived 31070 clauses, backtracked 6417 clauses, performed 88 splits and kept 18011 clauses.
% 25.36/25.54 SPASS allocated 105594 KBytes.
% 25.36/25.54 SPASS spent 0:0:18.34 on the problem.
% 25.36/25.54 0:00:00.04 for the input.
% 25.36/25.54 0:00:00.00 for the FLOTTER CNF translation.
% 25.36/25.54 0:00:00.31 for inferences.
% 25.36/25.54 0:00:00.68 for the backtracking.
% 25.36/25.54 0:0:16.93 for the reduction.
% 25.36/25.54
% 25.36/25.54
% 25.36/25.54 Here is a proof with depth 2, length 45 :
% 25.36/25.54 % SZS output start Refutation
% See solution above
% 25.36/25.54 Formulae used in the proof : co1_1 co1_6 co1_7 co1_11 co1_12 co1_14 co1_15 co1_16 clause47 clause72 clause85 clause86 clause103 clause157 clause179
% 25.36/25.54
%------------------------------------------------------------------------------