TSTP Solution File: SWC153-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC153-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 22:02:06 EDT 2022
% Result : Unsatisfiable 34.33s 34.57s
% Output : Refutation 34.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of clauses : 62 ( 20 unt; 1 nHn; 62 RR)
% Number of literals : 206 ( 0 equ; 154 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
equal(sk1,sk3),
file('SWC153-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssItem(x)
| ~ ssItem(y)
| ~ leq(x,y)
| ~ equal(app(app(app(app(w,cons(y,nil)),v),cons(x,nil)),u),sk3)
| leq(y,x) ),
file('SWC153-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssItem(y)
| ~ ssItem(z)
| ~ memberP(w,u)
| ~ leq(y,z)
| ~ equal(app(app(app(app(x,cons(z,nil)),w),cons(y,nil)),v),sk3)
| leq(z,u) ),
file('SWC153-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x)
| ~ ssItem(y)
| ~ ssItem(z)
| ~ memberP(w,u)
| ~ leq(y,z)
| ~ equal(app(app(app(app(x,cons(z,nil)),w),cons(y,nil)),v),sk3)
| leq(u,y) ),
file('SWC153-1.p',unknown),
[] ).
cnf(12,axiom,
ssList(sk7),
file('SWC153-1.p',unknown),
[] ).
cnf(13,axiom,
ssList(sk8),
file('SWC153-1.p',unknown),
[] ).
cnf(14,axiom,
ssList(sk9),
file('SWC153-1.p',unknown),
[] ).
cnf(15,axiom,
equal(app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),sk1),
file('SWC153-1.p',unknown),
[] ).
cnf(16,axiom,
leq(sk6,sk5),
file('SWC153-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ leq(sk5,sk6)
| memberP(sk8,sk10) ),
file('SWC153-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ leq(sk5,sk6)
| ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
file('SWC153-1.p',unknown),
[] ).
cnf(31,axiom,
ssItem(skaf83(u)),
file('SWC153-1.p',unknown),
[] ).
cnf(81,axiom,
( ~ ssItem(u)
| leq(u,u) ),
file('SWC153-1.p',unknown),
[] ).
cnf(91,axiom,
( ~ ssList(u)
| ssItem(v)
| duplicatefreeP(u) ),
file('SWC153-1.p',unknown),
[] ).
cnf(104,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ssList(app(u,v)) ),
file('SWC153-1.p',unknown),
[] ).
cnf(105,axiom,
( ~ ssList(u)
| ~ ssItem(v)
| ssList(cons(v,u)) ),
file('SWC153-1.p',unknown),
[] ).
cnf(149,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ leq(u,v)
| ~ leq(v,u)
| equal(u,v) ),
file('SWC153-1.p',unknown),
[] ).
cnf(175,axiom,
( ~ ssItem(u)
| ~ ssItem(v)
| ~ ssItem(w)
| ~ leq(u,v)
| ~ leq(v,w)
| leq(u,w) ),
file('SWC153-1.p',unknown),
[] ).
cnf(176,axiom,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssItem(w)
| equal(app(cons(w,v),u),cons(w,app(v,u))) ),
file('SWC153-1.p',unknown),
[] ).
cnf(198,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('SWC153-1.p',unknown),
[] ).
cnf(207,plain,
equal(app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk6,nil)),sk9),sk3),
inference(rew,[status(thm),theory(equality)],[6,15]),
[iquote('0:Rew:6.0,15.0')] ).
cnf(349,plain,
( ~ ssItem(u)
| ssList(cons(u,sk9)) ),
inference(res,[status(thm),theory(equality)],[14,105]),
[iquote('0:Res:14.0,105.1')] ).
cnf(572,plain,
ssItem(u),
inference(spt,[spt(split,[position(s1)])],[91]),
[iquote('1:Spt:91.1')] ).
cnf(573,plain,
leq(u,u),
inference(mrr,[status(thm)],[81,572]),
[iquote('1:MRR:81.0,572.0')] ).
cnf(641,plain,
( ~ leq(u,v)
| ~ leq(v,u)
| equal(u,v) ),
inference(mrr,[status(thm)],[149,572]),
[iquote('1:MRR:149.1,149.0,572.0')] ).
cnf(669,plain,
( ~ leq(u,v)
| ~ leq(v,w)
| leq(u,w) ),
inference(mrr,[status(thm)],[175,572]),
[iquote('1:MRR:175.2,175.1,175.0,572.0')] ).
cnf(709,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ memberP(v,x)
| ~ leq(y,z)
| ~ equal(app(app(app(app(w,cons(z,nil)),v),cons(y,nil)),u),sk3)
| leq(x,y) ),
inference(mrr,[status(thm)],[9,572]),
[iquote('1:MRR:9.5,9.4,9.0,572.0')] ).
cnf(710,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ memberP(v,x)
| ~ leq(y,z)
| ~ equal(app(app(app(app(w,cons(z,nil)),v),cons(y,nil)),u),sk3)
| leq(z,x) ),
inference(mrr,[status(thm)],[8,572]),
[iquote('1:MRR:8.5,8.4,8.0,572.0')] ).
cnf(788,plain,
( ~ ssList(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ leq(x,y)
| ~ equal(app(app(app(app(w,cons(y,nil)),v),cons(x,nil)),u),sk3)
| leq(y,x) ),
inference(mrr,[status(thm)],[7,572]),
[iquote('1:MRR:7.4,7.3,572.0')] ).
cnf(789,plain,
( ~ leq(sk5,sk10)
| ~ leq(sk10,sk6) ),
inference(mrr,[status(thm)],[19,669]),
[iquote('1:MRR:19.0,669.2')] ).
cnf(2754,plain,
( ~ leq(sk5,sk6)
| equal(sk6,sk5) ),
inference(res,[status(thm),theory(equality)],[16,641]),
[iquote('1:Res:16.0,641.0')] ).
cnf(6567,plain,
( ~ ssList(sk9)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ leq(sk6,sk5)
| ~ equal(sk3,sk3)
| leq(sk5,sk6) ),
inference(spl,[status(thm),theory(equality)],[207,788]),
[iquote('1:SpL:207.0,788.4')] ).
cnf(6570,plain,
( ~ ssList(sk9)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ leq(sk6,sk5)
| leq(sk5,sk6) ),
inference(obv,[status(thm),theory(equality)],[6567]),
[iquote('1:Obv:6567.4')] ).
cnf(22744,plain,
( ~ leq(sk6,sk5)
| leq(sk5,sk6) ),
inference(ssi,[status(thm)],[6570,12,13,14]),
[iquote('1:SSi:6570.2,6570.1,6570.0,12.0,13.0,14.0')] ).
cnf(22745,plain,
leq(sk5,sk6),
inference(mrr,[status(thm)],[22744,16]),
[iquote('1:MRR:22744.0,16.0')] ).
cnf(22746,plain,
memberP(sk8,sk10),
inference(mrr,[status(thm)],[18,22745]),
[iquote('1:MRR:18.0,22745.0')] ).
cnf(22747,plain,
equal(sk6,sk5),
inference(mrr,[status(thm)],[2754,22745]),
[iquote('1:MRR:2754.0,22745.0')] ).
cnf(22753,plain,
( ~ leq(sk5,sk10)
| ~ leq(sk10,sk5) ),
inference(rew,[status(thm),theory(equality)],[22747,789]),
[iquote('1:Rew:22747.0,789.1')] ).
cnf(22764,plain,
equal(app(app(app(app(sk7,cons(sk5,nil)),sk8),cons(sk5,nil)),sk9),sk3),
inference(rew,[status(thm),theory(equality)],[22747,207]),
[iquote('1:Rew:22747.0,207.0')] ).
cnf(23020,plain,
( ~ ssList(sk9)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ memberP(sk8,u)
| ~ leq(sk5,sk5)
| ~ equal(sk3,sk3)
| leq(sk5,u) ),
inference(spl,[status(thm),theory(equality)],[22764,710]),
[iquote('1:SpL:22764.0,710.5')] ).
cnf(23021,plain,
( ~ ssList(sk9)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ memberP(sk8,u)
| ~ leq(sk5,sk5)
| ~ equal(sk3,sk3)
| leq(u,sk5) ),
inference(spl,[status(thm),theory(equality)],[22764,709]),
[iquote('1:SpL:22764.0,709.5')] ).
cnf(23030,plain,
( ~ ssList(sk9)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ memberP(sk8,u)
| ~ leq(sk5,sk5)
| leq(u,sk5) ),
inference(obv,[status(thm),theory(equality)],[23021]),
[iquote('1:Obv:23021.5')] ).
cnf(23033,plain,
( ~ ssList(sk9)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ memberP(sk8,u)
| ~ leq(sk5,sk5)
| leq(sk5,u) ),
inference(obv,[status(thm),theory(equality)],[23020]),
[iquote('1:Obv:23020.5')] ).
cnf(25066,plain,
( ~ memberP(sk8,u)
| ~ leq(sk5,sk5)
| leq(sk5,u) ),
inference(ssi,[status(thm)],[23033,12,13,14]),
[iquote('1:SSi:23033.2,23033.1,23033.0,12.0,13.0,14.0')] ).
cnf(25067,plain,
( ~ memberP(sk8,u)
| leq(sk5,u) ),
inference(mrr,[status(thm)],[25066,573]),
[iquote('1:MRR:25066.1,573.0')] ).
cnf(25068,plain,
( ~ memberP(sk8,u)
| ~ leq(sk5,sk5)
| leq(u,sk5) ),
inference(ssi,[status(thm)],[23030,12,13,14]),
[iquote('1:SSi:23030.2,23030.1,23030.0,12.0,13.0,14.0')] ).
cnf(25069,plain,
( ~ memberP(sk8,u)
| leq(u,sk5) ),
inference(mrr,[status(thm)],[25068,573]),
[iquote('1:MRR:25068.1,573.0')] ).
cnf(25175,plain,
leq(sk5,sk10),
inference(res,[status(thm),theory(equality)],[22746,25067]),
[iquote('1:Res:22746.0,25067.0')] ).
cnf(25176,plain,
~ leq(sk10,sk5),
inference(mrr,[status(thm)],[22753,25175]),
[iquote('1:MRR:22753.0,25175.0')] ).
cnf(25180,plain,
leq(sk10,sk5),
inference(res,[status(thm),theory(equality)],[22746,25069]),
[iquote('1:Res:22746.0,25069.0')] ).
cnf(25181,plain,
$false,
inference(mrr,[status(thm)],[25180,25176]),
[iquote('1:MRR:25180.0,25176.0')] ).
cnf(25182,plain,
( ~ ssList(u)
| duplicatefreeP(u) ),
inference(spt,[spt(split,[position(s2)])],[91]),
[iquote('1:Spt:25181.0,91.0,91.2')] ).
cnf(25200,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)],[198,25182]),
[iquote('1:MRR:198.1,25182.1')] ).
cnf(43560,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)],[176,104]),
[iquote('0:SpR:176.3,104.2')] ).
cnf(43612,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(cons(v,u))
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(obv,[status(thm),theory(equality)],[43560]),
[iquote('0:Obv:43560.0')] ).
cnf(43613,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w)
| ssList(cons(v,app(u,w))) ),
inference(ssi,[status(thm)],[43612,105]),
[iquote('0:SSi:43612.2,105.2')] ).
cnf(45181,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)],[25200]),
[iquote('1:EqR:25200.5')] ).
cnf(45219,plain,
( ~ ssItem(u)
| ~ ssList(v)
| ~ ssList(w)
| ~ ssList(x) ),
inference(ssi,[status(thm)],[45181,104,105]),
[iquote('1:SSi:45181.0,104.2,104.2,105.2,105.2')] ).
cnf(45220,plain,
( ~ ssList(u)
| ~ ssItem(v)
| ~ ssList(w) ),
inference(mrr,[status(thm)],[43613,45219]),
[iquote('1:MRR:43613.3,45219.1')] ).
cnf(45223,plain,
( ~ ssList(u)
| ~ ssItem(v) ),
inference(con,[status(thm)],[45220]),
[iquote('1:Con:45220.2')] ).
cnf(45225,plain,
~ ssItem(u),
inference(mrr,[status(thm)],[349,45223]),
[iquote('1:MRR:349.1,45223.0')] ).
cnf(45227,plain,
$false,
inference(unc,[status(thm)],[45225,31]),
[iquote('1:UnC:45225.0,31.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC153-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.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 23:52:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 34.33/34.57
% 34.33/34.57 SPASS V 3.9
% 34.33/34.57 SPASS beiseite: Proof found.
% 34.33/34.57 % SZS status Theorem
% 34.33/34.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.33/34.57 SPASS derived 29813 clauses, backtracked 16234 clauses, performed 331 splits and kept 22577 clauses.
% 34.33/34.57 SPASS allocated 108196 KBytes.
% 34.33/34.57 SPASS spent 0:0:25.41 on the problem.
% 34.33/34.57 0:00:00.04 for the input.
% 34.33/34.57 0:00:00.00 for the FLOTTER CNF translation.
% 34.33/34.57 0:00:00.30 for inferences.
% 34.33/34.57 0:00:00.71 for the backtracking.
% 34.33/34.57 0:0:23.96 for the reduction.
% 34.33/34.57
% 34.33/34.57
% 34.33/34.57 Here is a proof with depth 2, length 62 :
% 34.33/34.57 % SZS output start Refutation
% See solution above
% 34.33/34.57 Formulae used in the proof : co1_6 co1_7 co1_8 co1_9 co1_12 co1_13 co1_14 co1_15 co1_16 co1_18 co1_19 clause12 clause62 clause72 clause85 clause86 clause130 clause156 clause157 clause179
% 34.33/34.57
%------------------------------------------------------------------------------