%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT169+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:37:04 PM UTC 2026
% Result : Theorem 15.24s 8.13s
% Output : Refutation 16.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 27
% Syntax : Number of formulae : 209 ( 51 unt; 10 def)
% Number of atoms : 663 ( 153 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 814 ( 360 ~; 354 |; 75 &)
% ( 20 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 15 con; 0-4 aty)
% Number of variables : 255 ( 0 sgn 233 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
is_Arr1861959080le_alt(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_a) ).
fof(f17,axiom,
is_Arr1861959080le_alt(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_b) ).
fof(f18,axiom,
? [X0,X1,X2] :
( is_Arr1861959080le_alt(X0)
& is_Arr1861959080le_alt(X1)
& is_Arr1861959080le_alt(X2)
& hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X2),nil_Ar126264853le_alt))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_alt3) ).
fof(f19,axiom,
hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,nil_Ar126264853le_alt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_distinct_Osimps_I1_J) ).
fof(f144,axiom,
! [X0,X1,X2,X3] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3)
<=> ( ( X2 = nil_Ar126264853le_alt
& hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = X3 )
| ? [X4] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X4) = X2
& X1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X4),X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Cons__eq__append__conv) ).
fof(f194,axiom,
! [X0,X1] :
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),X1))
<=> hBOOL(hAPP_A862370221t_bool(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_mem__def) ).
fof(f258,axiom,
! [X0] : ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,nil_Ar126264853le_alt),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_member__rec_I2_J) ).
fof(f264,axiom,
! [X0,X1,X2] :
( ( is_Arr1861959080le_alt(X0)
& is_Arr1861959080le_alt(X2) )
=> ( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2))
<=> ( X0 = X2
| hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,X1),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_member__rec_I1_J) ).
fof(f309,axiom,
! [X0,X1] :
( hAPP_A832564074le_alt(replic351609551le_alt(X0),X1) = nil_Ar126264853le_alt
<=> X0 = zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_replicate__empty) ).
fof(f346,axiom,
! [X0,X1,X2] :
( ( is_Arr1861959080le_alt(X0)
& is_Arr1861959080le_alt(X1) )
=> ( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X2))))
=> ( X0 = X1
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X2))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_set__ConsD) ).
fof(f361,axiom,
member345038890le_alt = set_Ar1565008694le_alt,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_member__set) ).
fof(f387,axiom,
! [X0,X1] :
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)))
<=> ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
& hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_distinct_Osimps_I2_J) ).
fof(f391,axiom,
! [X0,X1,X2] :
( ? [X3] :
( is_Arr1861959080le_alt(X3)
& hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
& hBOOL(hAPP_A862370221t_bool(X0,X3)) )
<=> ( hBOOL(hAPP_A862370221t_bool(X0,X2))
& X1 != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_Bex__set__replicate) ).
fof(f393,axiom,
! [X0,X1,X2] :
( ! [X3] :
( is_Arr1861959080le_alt(X3)
=> ( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
=> hBOOL(hAPP_A862370221t_bool(X0,X3)) ) )
<=> ( hBOOL(hAPP_A862370221t_bool(X0,X2))
| X1 = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_Ball__set__replicate) ).
fof(f416,axiom,
! [X0,X1] :
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
<=> ? [X2,X3] : X1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_in__set__conv__decomp) ).
fof(f1283,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1284,conjecture,
? [X0] : hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f1285,negated_conjecture,
~ ? [X0] : hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))))),
inference(negated_conjecture,[status(cth)],[f1284]) ).
fof(f1420,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2))
<=> ( X0 = X2
| hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,X1),X2)) ) )
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X2) ),
inference(ennf_transformation,[],[f264]) ).
fof(f1421,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2))
<=> ( X0 = X2
| hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,X1),X2)) ) )
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X2) ),
inference(flattening,[],[f1420]) ).
fof(f1481,plain,
! [X0,X1,X2] :
( X0 = X1
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X2)))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X2))))
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X1) ),
inference(ennf_transformation,[],[f346]) ).
fof(f1482,plain,
! [X0,X1,X2] :
( X0 = X1
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X2)))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X2))))
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X1) ),
inference(flattening,[],[f1481]) ).
fof(f1513,plain,
! [X0,X1,X2] :
( ! [X3] :
( hBOOL(hAPP_A862370221t_bool(X0,X3))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ is_Arr1861959080le_alt(X3) )
<=> ( hBOOL(hAPP_A862370221t_bool(X0,X2))
| X1 = zero_zero_nat ) ),
inference(ennf_transformation,[],[f393]) ).
fof(f1514,plain,
! [X0,X1,X2] :
( ! [X3] :
( hBOOL(hAPP_A862370221t_bool(X0,X3))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ is_Arr1861959080le_alt(X3) )
<=> ( hBOOL(hAPP_A862370221t_bool(X0,X2))
| X1 = zero_zero_nat ) ),
inference(flattening,[],[f1513]) ).
fof(f2140,plain,
! [X0] : ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))))),
inference(ennf_transformation,[],[f1285]) ).
fof(f2163,plain,
( is_Arr1861959080le_alt(sK11)
& is_Arr1861959080le_alt(sK12)
& is_Arr1861959080le_alt(sK13)
& hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt))))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f18]) ).
fof(f2242,plain,
! [X0,X1,X2,X3] :
( ( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3)
| ( ( nil_Ar126264853le_alt != X2
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != X3 )
& ! [X4] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X4) != X2
| hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X4),X3) != X1 ) ) )
& ( ( X2 = nil_Ar126264853le_alt
& hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = X3 )
| ? [X4] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X4) = X2
& X1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X4),X3) )
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3) ) ),
inference(nnf_transformation,[],[f144]) ).
fof(f2243,plain,
! [X0,X1,X2,X3] :
( ( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3)
| ( ( nil_Ar126264853le_alt != X2
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != X3 )
& ! [X4] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X4) != X2
| hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X4),X3) != X1 ) ) )
& ( ( X2 = nil_Ar126264853le_alt
& hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = X3 )
| ? [X4] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X4) = X2
& X1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X4),X3) )
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3) ) ),
inference(flattening,[],[f2242]) ).
fof(f2244,plain,
! [X0,X1,X2,X3] :
( ( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3)
| ( ( nil_Ar126264853le_alt != X2
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != X3 )
& ! [X4] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X4) != X2
| hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X4),X3) != X1 ) ) )
& ( ( X2 = nil_Ar126264853le_alt
& hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = X3 )
| ? [X5] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X5) = X2
& hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X5),X3) = X1 )
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3) ) ),
inference(rectify,[],[f2243]) ).
fof(f2245,plain,
! [X0,X1,X2,X3] :
( ( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3)
| ( ( nil_Ar126264853le_alt != X2
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != X3 )
& ! [X4] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X4) != X2
| hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X4),X3) != X1 ) ) )
& ( ( X2 = nil_Ar126264853le_alt
& hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = X3 )
| ( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),sK41(X0,X1,X2,X3)) = X2
& hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,sK41(X0,X1,X2,X3)),X3) = X1 )
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(X5,sK41(X0,X1,X2,X3))],[f2244]) ).
fof(f2277,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),X1))
| ~ hBOOL(hAPP_A862370221t_bool(X1,X0)) )
& ( hBOOL(hAPP_A862370221t_bool(X1,X0))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),X1)) ) ),
inference(nnf_transformation,[],[f194]) ).
fof(f2302,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2))
| ( X0 != X2
& ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,X1),X2)) ) )
& ( X0 = X2
| hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,X1),X2))
| ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2)) ) )
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X2) ),
inference(nnf_transformation,[],[f1421]) ).
fof(f2303,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2))
| ( X0 != X2
& ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,X1),X2)) ) )
& ( X0 = X2
| hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,X1),X2))
| ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2)) ) )
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X2) ),
inference(flattening,[],[f2302]) ).
fof(f2351,plain,
! [X0,X1] :
( ( hAPP_A832564074le_alt(replic351609551le_alt(X0),X1) = nil_Ar126264853le_alt
| zero_zero_nat != X0 )
& ( X0 = zero_zero_nat
| nil_Ar126264853le_alt != hAPP_A832564074le_alt(replic351609551le_alt(X0),X1) ) ),
inference(nnf_transformation,[],[f309]) ).
fof(f2395,plain,
! [X0,X1] :
( ( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)))
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,X1)) )
& ( ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
& hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,X1)) )
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1))) ) ),
inference(nnf_transformation,[],[f387]) ).
fof(f2396,plain,
! [X0,X1] :
( ( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)))
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,X1)) )
& ( ( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
& hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,X1)) )
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1))) ) ),
inference(flattening,[],[f2395]) ).
fof(f2403,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( is_Arr1861959080le_alt(X3)
& hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
& hBOOL(hAPP_A862370221t_bool(X0,X3)) )
| ~ hBOOL(hAPP_A862370221t_bool(X0,X2))
| zero_zero_nat = X1 )
& ( ( hBOOL(hAPP_A862370221t_bool(X0,X2))
& X1 != zero_zero_nat )
| ! [X3] :
( ~ is_Arr1861959080le_alt(X3)
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ hBOOL(hAPP_A862370221t_bool(X0,X3)) ) ) ),
inference(nnf_transformation,[],[f391]) ).
fof(f2404,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( is_Arr1861959080le_alt(X3)
& hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
& hBOOL(hAPP_A862370221t_bool(X0,X3)) )
| ~ hBOOL(hAPP_A862370221t_bool(X0,X2))
| zero_zero_nat = X1 )
& ( ( hBOOL(hAPP_A862370221t_bool(X0,X2))
& X1 != zero_zero_nat )
| ! [X3] :
( ~ is_Arr1861959080le_alt(X3)
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ hBOOL(hAPP_A862370221t_bool(X0,X3)) ) ) ),
inference(flattening,[],[f2403]) ).
fof(f2405,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( is_Arr1861959080le_alt(X3)
& hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
& hBOOL(hAPP_A862370221t_bool(X0,X3)) )
| ~ hBOOL(hAPP_A862370221t_bool(X0,X2))
| zero_zero_nat = X1 )
& ( ( hBOOL(hAPP_A862370221t_bool(X0,X2))
& X1 != zero_zero_nat )
| ! [X4] :
( ~ is_Arr1861959080le_alt(X4)
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ hBOOL(hAPP_A862370221t_bool(X0,X4)) ) ) ),
inference(rectify,[],[f2404]) ).
fof(f2406,plain,
! [X0,X1,X2] :
( ( ( is_Arr1861959080le_alt(sK132(X0,X1,X2))
& hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,sK132(X0,X1,X2)),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
& hBOOL(hAPP_A862370221t_bool(X0,sK132(X0,X1,X2))) )
| ~ hBOOL(hAPP_A862370221t_bool(X0,X2))
| zero_zero_nat = X1 )
& ( ( hBOOL(hAPP_A862370221t_bool(X0,X2))
& X1 != zero_zero_nat )
| ! [X4] :
( ~ is_Arr1861959080le_alt(X4)
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ hBOOL(hAPP_A862370221t_bool(X0,X4)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(X3,sK132(X0,X1,X2))],[f2405]) ).
fof(f2411,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP_A862370221t_bool(X0,X3))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ is_Arr1861959080le_alt(X3) )
| ( ~ hBOOL(hAPP_A862370221t_bool(X0,X2))
& zero_zero_nat != X1 ) )
& ( hBOOL(hAPP_A862370221t_bool(X0,X2))
| X1 = zero_zero_nat
| ? [X3] :
( ~ hBOOL(hAPP_A862370221t_bool(X0,X3))
& hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
& is_Arr1861959080le_alt(X3) ) ) ),
inference(nnf_transformation,[],[f1514]) ).
fof(f2412,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP_A862370221t_bool(X0,X3))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ is_Arr1861959080le_alt(X3) )
| ( ~ hBOOL(hAPP_A862370221t_bool(X0,X2))
& zero_zero_nat != X1 ) )
& ( hBOOL(hAPP_A862370221t_bool(X0,X2))
| X1 = zero_zero_nat
| ? [X3] :
( ~ hBOOL(hAPP_A862370221t_bool(X0,X3))
& hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
& is_Arr1861959080le_alt(X3) ) ) ),
inference(flattening,[],[f2411]) ).
fof(f2413,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP_A862370221t_bool(X0,X3))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ is_Arr1861959080le_alt(X3) )
| ( ~ hBOOL(hAPP_A862370221t_bool(X0,X2))
& zero_zero_nat != X1 ) )
& ( hBOOL(hAPP_A862370221t_bool(X0,X2))
| X1 = zero_zero_nat
| ? [X4] :
( ~ hBOOL(hAPP_A862370221t_bool(X0,X4))
& hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
& is_Arr1861959080le_alt(X4) ) ) ),
inference(rectify,[],[f2412]) ).
fof(f2414,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP_A862370221t_bool(X0,X3))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ is_Arr1861959080le_alt(X3) )
| ( ~ hBOOL(hAPP_A862370221t_bool(X0,X2))
& zero_zero_nat != X1 ) )
& ( hBOOL(hAPP_A862370221t_bool(X0,X2))
| X1 = zero_zero_nat
| ( ~ hBOOL(hAPP_A862370221t_bool(X0,sK134(X0,X1,X2)))
& hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,sK134(X0,X1,X2)),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
& is_Arr1861959080le_alt(sK134(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(X4,sK134(X0,X1,X2))],[f2413]) ).
fof(f2432,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
| ! [X2,X3] : hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X3)) != X1 )
& ( ? [X2,X3] : X1 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X3))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1))) ) ),
inference(nnf_transformation,[],[f416]) ).
fof(f2433,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
| ! [X2,X3] : hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X3)) != X1 )
& ( ? [X4,X5] : hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X4),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X5)) = X1
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1))) ) ),
inference(rectify,[],[f2432]) ).
fof(f2434,plain,
! [X0,X1] :
( ( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
| ! [X2,X3] : hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X3)) != X1 )
& ( hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,sK144(X0,X1)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),sK145(X0,X1))) = X1
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144,sK145]),skolemize(X4,sK144(X0,X1)),skolemize(X5,sK145(X0,X1))],[f2433]) ).
fof(f2907,plain,
is_Arr1861959080le_alt(a),
inference(cnf_transformation,[],[f16]) ).
fof(f2908,plain,
is_Arr1861959080le_alt(b),
inference(cnf_transformation,[],[f17]) ).
fof(f2909,plain,
hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt))))),
inference(cnf_transformation,[],[f2163]) ).
fof(f2910,plain,
is_Arr1861959080le_alt(sK13),
inference(cnf_transformation,[],[f2163]) ).
fof(f2911,plain,
is_Arr1861959080le_alt(sK12),
inference(cnf_transformation,[],[f2163]) ).
fof(f2912,plain,
is_Arr1861959080le_alt(sK11),
inference(cnf_transformation,[],[f2163]) ).
fof(f2913,plain,
hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,nil_Ar126264853le_alt)),
inference(cnf_transformation,[],[f19]) ).
fof(f3146,plain,
! [X2,X3,X0,X1] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),X3)
| nil_Ar126264853le_alt != X2
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != X3 ),
inference(cnf_transformation,[],[f2245]) ).
fof(f3245,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),X1))
| hBOOL(hAPP_A862370221t_bool(X1,X0)) ),
inference(cnf_transformation,[],[f2277]) ).
fof(f3246,plain,
! [X0,X1] :
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),X1))
| ~ hBOOL(hAPP_A862370221t_bool(X1,X0)) ),
inference(cnf_transformation,[],[f2277]) ).
fof(f3332,plain,
! [X0] : ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,nil_Ar126264853le_alt),X0)),
inference(cnf_transformation,[],[f258]) ).
fof(f3343,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2))
| ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,X1),X2))
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X2) ),
inference(cnf_transformation,[],[f2303]) ).
fof(f3344,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2))
| X0 != X2
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X2) ),
inference(cnf_transformation,[],[f2303]) ).
fof(f3464,plain,
! [X0,X1] :
( nil_Ar126264853le_alt = hAPP_A832564074le_alt(replic351609551le_alt(X0),X1)
| zero_zero_nat != X0 ),
inference(cnf_transformation,[],[f2351]) ).
fof(f3548,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X2))))
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X2)))
| X0 = X1
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X1) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f3570,plain,
member345038890le_alt = set_Ar1565008694le_alt,
inference(cnf_transformation,[],[f361]) ).
fof(f3617,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)))
| hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,X1)) ),
inference(cnf_transformation,[],[f2396]) ).
fof(f3618,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1))) ),
inference(cnf_transformation,[],[f2396]) ).
fof(f3619,plain,
! [X0,X1] :
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)))
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,X1)) ),
inference(cnf_transformation,[],[f2396]) ).
fof(f3629,plain,
! [X2,X0,X1,X4] :
( zero_zero_nat != X1
| ~ is_Arr1861959080le_alt(X4)
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ hBOOL(hAPP_A862370221t_bool(X0,X4)) ),
inference(cnf_transformation,[],[f2406]) ).
fof(f3641,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP_A862370221t_bool(X0,X3))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(X1),X2))))
| ~ is_Arr1861959080le_alt(X3)
| zero_zero_nat != X1 ),
inference(cnf_transformation,[],[f2414]) ).
fof(f3683,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1)))
| hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X3)) != X1 ),
inference(cnf_transformation,[],[f2434]) ).
fof(f5075,plain,
a != b,
inference(cnf_transformation,[],[f1283]) ).
fof(f5076,plain,
! [X0] : ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))))),
inference(cnf_transformation,[],[f2140]) ).
fof(f5170,plain,
! [X0] : ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt),X0)),
inference(definition_unfolding,[],[f3332,f3570]) ).
fof(f5172,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2))
| X0 != X2
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X2) ),
inference(definition_unfolding,[],[f3344,f3570]) ).
fof(f5173,plain,
! [X2,X0,X1] :
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X2))
| ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1),X2))
| ~ is_Arr1861959080le_alt(X0)
| ~ is_Arr1861959080le_alt(X2) ),
inference(definition_unfolding,[],[f3343,f3570,f3570]) ).
fof(f5336,plain,
! [X3,X0,X1] :
( hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,nil_Ar126264853le_alt),X3)
| hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) != X3 ),
inference(equality_resolution,[],[f3146]) ).
fof(f5337,plain,
! [X0,X1] : hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,nil_Ar126264853le_alt),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),
inference(equality_resolution,[],[f5336]) ).
fof(f5384,plain,
! [X2,X1] :
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X2),X1)),X2))
| ~ is_Arr1861959080le_alt(X2)
| ~ is_Arr1861959080le_alt(X2) ),
inference(equality_resolution,[],[f5172]) ).
fof(f5408,plain,
! [X1] : nil_Ar126264853le_alt = hAPP_A832564074le_alt(replic351609551le_alt(zero_zero_nat),X1),
inference(equality_resolution,[],[f3464]) ).
fof(f5428,plain,
! [X2,X0,X4] :
( ~ is_Arr1861959080le_alt(X4)
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(zero_zero_nat),X2))))
| ~ hBOOL(hAPP_A862370221t_bool(X0,X4)) ),
inference(equality_resolution,[],[f3629]) ).
fof(f5430,plain,
! [X2,X3,X0] :
( hBOOL(hAPP_A862370221t_bool(X0,X3))
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X3),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(zero_zero_nat),X2))))
| ~ is_Arr1861959080le_alt(X3) ),
inference(equality_resolution,[],[f3641]) ).
fof(f5433,plain,
! [X2,X3,X0] : hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,X2),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X3))))),
inference(equality_resolution,[],[f3683]) ).
fof(f5628,definition,
sF411 = hAPP_A408086601le_alt(cons_A1216297413le_alt,a),
introduced(definition,[new_symbols(definition,[sF411])],[function_definition]) ).
fof(f5629,plain,
hAPP_A408086601le_alt(cons_A1216297413le_alt,a) = sF411,
inference(reorient_equations,[],[f5628]) ).
fof(f5630,definition,
sF412 = hAPP_A408086601le_alt(cons_A1216297413le_alt,b),
introduced(definition,[new_symbols(definition,[sF412])],[function_definition]) ).
fof(f5631,plain,
hAPP_A408086601le_alt(cons_A1216297413le_alt,b) = sF412,
inference(reorient_equations,[],[f5630]) ).
fof(f5632,plain,
! [X0] : ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))))),
inference(definition_folding,[],[f5076,f5631,f5629]) ).
fof(f5647,plain,
! [X2,X1] :
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X2),X1)),X2))
| ~ is_Arr1861959080le_alt(X2) ),
inference(duplicate_literal_removal,[],[f5384]) ).
fof(f5745,plain,
! [X2,X4] :
( ~ is_Arr1861959080le_alt(X4)
| ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(zero_zero_nat),X2)))) ),
inference(forward_subsumption_resolution,[],[f5428,f5430]) ).
fof(f5770,plain,
! [X4] :
( ~ hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt)))
| ~ is_Arr1861959080le_alt(X4) ),
inference(forward_demodulation,[],[f5745,f5408]) ).
fof(f5798,plain,
~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(sF411,nil_Ar126264853le_alt))))),
inference(superposition,[],[f5632,f5629]) ).
fof(f5800,plain,
hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt)))),
inference(resolution,[],[f3617,f2909]) ).
fof(f5804,plain,
! [X0] :
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,a),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0)))
| hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,X0)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,X0)) ),
inference(superposition,[],[f3619,f5629]) ).
fof(f5805,plain,
! [X0] :
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,b),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0)))
| hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,X0)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,X0)) ),
inference(superposition,[],[f3619,f5631]) ).
fof(f5810,plain,
hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt))),
inference(resolution,[],[f5800,f3617]) ).
fof(f5818,plain,
! [X0,X1] :
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,a),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0)))
| a = X1
| ~ is_Arr1861959080le_alt(a)
| ~ is_Arr1861959080le_alt(X1)
| hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X0))))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X0))) ),
inference(resolution,[],[f3548,f5804]) ).
fof(f5819,plain,
! [X0,X1] :
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,b),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0)))
| b = X1
| ~ is_Arr1861959080le_alt(b)
| ~ is_Arr1861959080le_alt(X1)
| hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X0))))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X0))) ),
inference(resolution,[],[f3548,f5805]) ).
fof(f5825,plain,
! [X0,X1] :
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X0))))
| b = X1
| ~ is_Arr1861959080le_alt(X1)
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,b),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X0))) ),
inference(forward_subsumption_resolution,[],[f5819,f2908]) ).
fof(f5826,plain,
! [X0,X1] :
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X0))))
| a = X1
| ~ is_Arr1861959080le_alt(X1)
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,a),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X1),X0))) ),
inference(forward_subsumption_resolution,[],[f5818,f2907]) ).
fof(f5828,plain,
! [X0] :
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,X0))))
| a = b
| ~ is_Arr1861959080le_alt(b)
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,a),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,X0))) ),
inference(superposition,[],[f5826,f5631]) ).
fof(f5829,plain,
! [X0] :
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,X0))))
| ~ is_Arr1861959080le_alt(b)
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,a),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,X0))) ),
inference(forward_subsumption_resolution,[],[f5828,f5075]) ).
fof(f5830,plain,
! [X0] :
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,X0))))
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,a),hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,X0))) ),
inference(forward_subsumption_resolution,[],[f5829,f2908]) ).
fof(f5831,plain,
! [X0] :
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,a),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt)))) ),
inference(resolution,[],[f5830,f5632]) ).
fof(f5853,plain,
! [X0] :
( ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))))
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,a),hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt)))
| a = X0
| ~ is_Arr1861959080le_alt(a)
| ~ is_Arr1861959080le_alt(X0) ),
inference(resolution,[],[f5831,f3548]) ).
fof(f5856,plain,
! [X0] :
( ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))))
| a = X0
| ~ is_Arr1861959080le_alt(a)
| ~ is_Arr1861959080le_alt(X0) ),
inference(forward_subsumption_resolution,[],[f5853,f5770]) ).
fof(f5857,plain,
! [X0] :
( ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))))
| a = X0
| ~ is_Arr1861959080le_alt(X0) ),
inference(forward_subsumption_resolution,[],[f5856,f2907]) ).
fof(f5869,definition,
( spl413_12
<=> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,b),hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt))) ),
introduced(definition,[new_symbols(definition,[spl413_12])],[avatar_definition]) ).
fof(f5871,plain,
( hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,b),hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt)))
| ~ spl413_12 ),
inference(avatar_component_clause,[],[f5869]) ).
fof(f5878,plain,
! [X0,X1] : hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)))),
inference(superposition,[],[f5433,f5337]) ).
fof(f5895,plain,
! [X0] : hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,a),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(sF411,X0)))),
inference(superposition,[],[f5878,f5629]) ).
fof(f5901,plain,
! [X0,X1] :
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(sF411,X0)),X1))
| ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0),X1))
| ~ is_Arr1861959080le_alt(a)
| ~ is_Arr1861959080le_alt(X1) ),
inference(superposition,[],[f5173,f5629]) ).
fof(f5904,plain,
! [X0,X1] :
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(sF411,X0)),X1))
| ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,X0),X1))
| ~ is_Arr1861959080le_alt(X1) ),
inference(forward_subsumption_resolution,[],[f5901,f2907]) ).
fof(f5905,plain,
! [X0] :
( a = X0
| ~ is_Arr1861959080le_alt(X0)
| b = X0
| ~ is_Arr1861959080le_alt(X0)
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,b),hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))) ),
inference(resolution,[],[f5857,f5825]) ).
fof(f5907,plain,
! [X0] :
( a = X0
| ~ is_Arr1861959080le_alt(X0)
| b = X0
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,b),hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt))) ),
inference(duplicate_literal_removal,[],[f5905]) ).
fof(f5909,definition,
( spl413_13
<=> ! [X0] :
( a = X0
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt)))
| b = X0
| ~ is_Arr1861959080le_alt(X0) ) ),
introduced(definition,[new_symbols(definition,[spl413_13])],[avatar_definition]) ).
fof(f5910,plain,
( ! [X0] :
( ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),nil_Ar126264853le_alt)))
| a = X0
| b = X0
| ~ is_Arr1861959080le_alt(X0) )
| ~ spl413_13 ),
inference(avatar_component_clause,[],[f5909]) ).
fof(f5911,plain,
( spl413_12
| spl413_13 ),
inference(avatar_split_clause,[],[f5907,f5909,f5869]) ).
fof(f5930,plain,
! [X0,X1] : hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)),X0)),
inference(resolution,[],[f3245,f5878]) ).
fof(f5932,plain,
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt),b))
| ~ spl413_12 ),
inference(resolution,[],[f3245,f5871]) ).
fof(f5934,plain,
( $false
| ~ spl413_12 ),
inference(forward_subsumption_resolution,[],[f5932,f5170]) ).
fof(f5935,plain,
~ spl413_12,
inference(avatar_contradiction_clause,[],[f5934]) ).
fof(f5939,plain,
( ! [X0] :
( a = X0
| b = X0
| ~ is_Arr1861959080le_alt(X0)
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt)))
| ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,nil_Ar126264853le_alt)) )
| ~ spl413_13 ),
inference(resolution,[],[f5910,f3619]) ).
fof(f5940,plain,
( a = sK13
| b = sK13
| ~ is_Arr1861959080le_alt(sK13)
| ~ spl413_13 ),
inference(resolution,[],[f5910,f5810]) ).
fof(f5942,plain,
( a = sK13
| b = sK13
| ~ spl413_13 ),
inference(forward_subsumption_resolution,[],[f5940,f2910]) ).
fof(f5943,plain,
( ! [X0] :
( a = X0
| b = X0
| ~ is_Arr1861959080le_alt(X0)
| hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X0),hAPP_l82377208t_bool(set_Ar1565008694le_alt,nil_Ar126264853le_alt))) )
| ~ spl413_13 ),
inference(forward_subsumption_resolution,[],[f5939,f2913]) ).
fof(f5945,definition,
( spl413_14
<=> b = sK13 ),
introduced(definition,[new_symbols(definition,[spl413_14])],[avatar_definition]) ).
fof(f5947,plain,
( b = sK13
| ~ spl413_14 ),
inference(avatar_component_clause,[],[f5945]) ).
fof(f5949,definition,
( spl413_15
<=> a = sK13 ),
introduced(definition,[new_symbols(definition,[spl413_15])],[avatar_definition]) ).
fof(f5951,plain,
( a = sK13
| ~ spl413_15 ),
inference(avatar_component_clause,[],[f5949]) ).
fof(f5952,plain,
( spl413_14
| spl413_15
| ~ spl413_13 ),
inference(avatar_split_clause,[],[f5942,f5909,f5949,f5945]) ).
fof(f5953,plain,
( ! [X0] :
( ~ is_Arr1861959080le_alt(X0)
| b = X0
| a = X0 )
| ~ spl413_13 ),
inference(forward_subsumption_resolution,[],[f5943,f5770]) ).
fof(f5970,plain,
! [X0,X1] :
( ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X0),X1)))
| ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,X1),X0)) ),
inference(resolution,[],[f3618,f3246]) ).
fof(f5981,plain,
~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt))),sK11)),
inference(resolution,[],[f5970,f2909]) ).
fof(f5982,plain,
~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt)),sK12)),
inference(resolution,[],[f5970,f5800]) ).
fof(f6131,plain,
! [X0] :
( hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(sF412,X0)),b))
| ~ is_Arr1861959080le_alt(b) ),
inference(superposition,[],[f5647,f5631]) ).
fof(f6132,plain,
! [X0] : hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(sF412,X0)),b)),
inference(forward_subsumption_resolution,[],[f6131,f2908]) ).
fof(f6135,plain,
! [X0] : ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(sF411,X0)))),
inference(resolution,[],[f5895,f3618]) ).
fof(f6137,plain,
! [X0] : ~ hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF411,X0)))),
inference(forward_demodulation,[],[f6135,f5629]) ).
fof(f6322,plain,
( b = sK11
| a = sK11
| ~ spl413_13 ),
inference(resolution,[],[f2912,f5953]) ).
fof(f6324,definition,
( spl413_16
<=> a = sK11 ),
introduced(definition,[new_symbols(definition,[spl413_16])],[avatar_definition]) ).
fof(f6326,plain,
( a = sK11
| ~ spl413_16 ),
inference(avatar_component_clause,[],[f6324]) ).
fof(f6328,definition,
( spl413_17
<=> b = sK11 ),
introduced(definition,[new_symbols(definition,[spl413_17])],[avatar_definition]) ).
fof(f6330,plain,
( b = sK11
| ~ spl413_17 ),
inference(avatar_component_clause,[],[f6328]) ).
fof(f6331,plain,
( spl413_16
| spl413_17
| ~ spl413_13 ),
inference(avatar_split_clause,[],[f6322,f5909,f6328,f6324]) ).
fof(f6503,plain,
( b = sK12
| a = sK12
| ~ spl413_13 ),
inference(resolution,[],[f2911,f5953]) ).
fof(f6505,definition,
( spl413_18
<=> a = sK12 ),
introduced(definition,[new_symbols(definition,[spl413_18])],[avatar_definition]) ).
fof(f6507,plain,
( a = sK12
| ~ spl413_18 ),
inference(avatar_component_clause,[],[f6505]) ).
fof(f6509,definition,
( spl413_19
<=> b = sK12 ),
introduced(definition,[new_symbols(definition,[spl413_19])],[avatar_definition]) ).
fof(f6511,plain,
( b = sK12
| ~ spl413_19 ),
inference(avatar_component_clause,[],[f6509]) ).
fof(f6512,plain,
( spl413_18
| spl413_19
| ~ spl413_13 ),
inference(avatar_split_clause,[],[f6503,f5909,f6509,f6505]) ).
fof(f6516,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt)))))
| ~ spl413_18 ),
inference(superposition,[],[f2909,f6507]) ).
fof(f6517,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),nil_Ar126264853le_alt)))))
| ~ spl413_14
| ~ spl413_18 ),
inference(forward_demodulation,[],[f6516,f5947]) ).
fof(f6520,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(sF412,nil_Ar126264853le_alt)))))
| ~ spl413_14
| ~ spl413_18 ),
inference(forward_demodulation,[],[f6517,f5631]) ).
fof(f6522,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,nil_Ar126264853le_alt)))))
| ~ spl413_14
| ~ spl413_18 ),
inference(forward_demodulation,[],[f6520,f5629]) ).
fof(f6524,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,nil_Ar126264853le_alt)))))
| ~ spl413_14
| ~ spl413_16
| ~ spl413_18 ),
inference(forward_demodulation,[],[f6522,f6326]) ).
fof(f6525,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,nil_Ar126264853le_alt)))))
| ~ spl413_14
| ~ spl413_16
| ~ spl413_18 ),
inference(forward_demodulation,[],[f6524,f5629]) ).
fof(f6526,plain,
( $false
| ~ spl413_14
| ~ spl413_16
| ~ spl413_18 ),
inference(forward_subsumption_resolution,[],[f6525,f6137]) ).
fof(f6527,plain,
( ~ spl413_14
| ~ spl413_16
| ~ spl413_18 ),
inference(avatar_contradiction_clause,[],[f6526]) ).
fof(f6528,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt)),a))
| ~ spl413_18 ),
inference(forward_demodulation,[],[f5982,f6507]) ).
fof(f6533,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),nil_Ar126264853le_alt)),a))
| ~ spl413_15
| ~ spl413_18 ),
inference(forward_demodulation,[],[f6528,f5951]) ).
fof(f6539,plain,
( $false
| ~ spl413_15
| ~ spl413_18 ),
inference(forward_subsumption_resolution,[],[f6533,f5930]) ).
fof(f6540,plain,
( ~ spl413_15
| ~ spl413_18 ),
inference(avatar_contradiction_clause,[],[f6539]) ).
fof(f6554,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt))),b))
| ~ spl413_17 ),
inference(forward_demodulation,[],[f5981,f6330]) ).
fof(f6558,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),nil_Ar126264853le_alt))),b))
| ~ spl413_14
| ~ spl413_17 ),
inference(forward_demodulation,[],[f6554,f5947]) ).
fof(f6562,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(sF412,nil_Ar126264853le_alt))),b))
| ~ spl413_14
| ~ spl413_17 ),
inference(forward_demodulation,[],[f6558,f5631]) ).
fof(f6565,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(sF412,nil_Ar126264853le_alt))),b))
| ~ spl413_14
| ~ spl413_17
| ~ spl413_18 ),
inference(forward_demodulation,[],[f6562,f6507]) ).
fof(f6567,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,nil_Ar126264853le_alt))),b))
| ~ spl413_14
| ~ spl413_17
| ~ spl413_18 ),
inference(forward_demodulation,[],[f6565,f5629]) ).
fof(f6589,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(sF412,nil_Ar126264853le_alt)),b))
| ~ is_Arr1861959080le_alt(b)
| ~ spl413_14
| ~ spl413_17
| ~ spl413_18 ),
inference(resolution,[],[f6567,f5904]) ).
fof(f6590,plain,
( ~ is_Arr1861959080le_alt(b)
| ~ spl413_14
| ~ spl413_17
| ~ spl413_18 ),
inference(forward_subsumption_resolution,[],[f6589,f6132]) ).
fof(f6591,plain,
( $false
| ~ spl413_14
| ~ spl413_17
| ~ spl413_18 ),
inference(forward_subsumption_resolution,[],[f6590,f2908]) ).
fof(f6592,plain,
( ~ spl413_14
| ~ spl413_17
| ~ spl413_18 ),
inference(avatar_contradiction_clause,[],[f6591]) ).
fof(f6593,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt)),b))
| ~ spl413_19 ),
inference(forward_demodulation,[],[f5982,f6511]) ).
fof(f6597,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),nil_Ar126264853le_alt)),b))
| ~ spl413_14
| ~ spl413_19 ),
inference(forward_demodulation,[],[f6593,f5947]) ).
fof(f6601,plain,
( $false
| ~ spl413_14
| ~ spl413_19 ),
inference(forward_subsumption_resolution,[],[f6597,f5930]) ).
fof(f6602,plain,
( ~ spl413_14
| ~ spl413_19 ),
inference(avatar_contradiction_clause,[],[f6601]) ).
fof(f6621,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),nil_Ar126264853le_alt)))))
| ~ spl413_15 ),
inference(superposition,[],[f2909,f5951]) ).
fof(f6622,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(sF411,nil_Ar126264853le_alt)))))
| ~ spl413_15 ),
inference(forward_demodulation,[],[f6621,f5629]) ).
fof(f6625,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),hAPP_l726444215le_alt(sF411,nil_Ar126264853le_alt)))))
| ~ spl413_15
| ~ spl413_19 ),
inference(forward_demodulation,[],[f6622,f6511]) ).
fof(f6629,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK11),hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(sF411,nil_Ar126264853le_alt)))))
| ~ spl413_15
| ~ spl413_19 ),
inference(forward_demodulation,[],[f6625,f5631]) ).
fof(f6631,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(sF411,nil_Ar126264853le_alt)))))
| ~ spl413_15
| ~ spl413_16
| ~ spl413_19 ),
inference(forward_demodulation,[],[f6629,f6326]) ).
fof(f6634,plain,
( hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(sF411,hAPP_l726444215le_alt(sF412,hAPP_l726444215le_alt(sF411,nil_Ar126264853le_alt)))))
| ~ spl413_15
| ~ spl413_16
| ~ spl413_19 ),
inference(forward_demodulation,[],[f6631,f5629]) ).
fof(f6635,plain,
( $false
| ~ spl413_15
| ~ spl413_16
| ~ spl413_19 ),
inference(forward_subsumption_resolution,[],[f6634,f5798]) ).
fof(f6636,plain,
( ~ spl413_15
| ~ spl413_16
| ~ spl413_19 ),
inference(avatar_contradiction_clause,[],[f6635]) ).
fof(f6637,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK13),nil_Ar126264853le_alt))),b))
| ~ spl413_17 ),
inference(forward_demodulation,[],[f5981,f6330]) ).
fof(f6639,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),nil_Ar126264853le_alt))),b))
| ~ spl413_15
| ~ spl413_17 ),
inference(forward_demodulation,[],[f6637,f5951]) ).
fof(f6641,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,sK12),hAPP_l726444215le_alt(sF411,nil_Ar126264853le_alt))),b))
| ~ spl413_15
| ~ spl413_17 ),
inference(forward_demodulation,[],[f6639,f5629]) ).
fof(f6644,plain,
( ~ hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),hAPP_l726444215le_alt(sF411,nil_Ar126264853le_alt))),b))
| ~ spl413_15
| ~ spl413_17
| ~ spl413_19 ),
inference(forward_demodulation,[],[f6641,f6511]) ).
fof(f6645,plain,
( $false
| ~ spl413_15
| ~ spl413_17
| ~ spl413_19 ),
inference(forward_subsumption_resolution,[],[f6644,f5930]) ).
fof(f6646,plain,
( ~ spl413_15
| ~ spl413_17
| ~ spl413_19 ),
inference(avatar_contradiction_clause,[],[f6645]) ).
cnf(s10,plain,
( spl413_12
| spl413_13 ),
inference(sat_conversion,[],[f5911]) ).
cnf(s11,plain,
~ spl413_12,
inference(sat_conversion,[],[f5935]) ).
cnf(s12,plain,
( ~ spl413_13
| spl413_14
| spl413_15 ),
inference(sat_conversion,[],[f5952]) ).
cnf(s13,plain,
( ~ spl413_13
| spl413_16
| spl413_17 ),
inference(sat_conversion,[],[f6331]) ).
cnf(s14,plain,
( ~ spl413_13
| spl413_18
| spl413_19 ),
inference(sat_conversion,[],[f6512]) ).
cnf(s15,plain,
( ~ spl413_14
| ~ spl413_16
| ~ spl413_18 ),
inference(sat_conversion,[],[f6527]) ).
cnf(s17,plain,
( ~ spl413_15
| ~ spl413_18 ),
inference(sat_conversion,[],[f6540]) ).
cnf(s21,plain,
( ~ spl413_14
| ~ spl413_17
| ~ spl413_18 ),
inference(sat_conversion,[],[f6592]) ).
cnf(s22,plain,
( ~ spl413_14
| ~ spl413_19 ),
inference(sat_conversion,[],[f6602]) ).
cnf(s27,plain,
( ~ spl413_15
| ~ spl413_16
| ~ spl413_19 ),
inference(sat_conversion,[],[f6636]) ).
cnf(s29,plain,
( ~ spl413_15
| ~ spl413_17
| ~ spl413_19 ),
inference(sat_conversion,[],[f6646]) ).
cnf(s30,plain,
spl413_13,
inference(rat,[],[s10,s11]) ).
cnf(s33,plain,
( ~ spl413_18
| ~ spl413_14 ),
inference(rat,[],[s13,s15,s21,s30]) ).
cnf(s34,plain,
~ spl413_14,
inference(rat,[],[s33,s14,s22,s30]) ).
cnf(s35,plain,
spl413_15,
inference(rat,[],[s12,s30,s34]) ).
cnf(s37,plain,
~ spl413_18,
inference(rat,[],[s17,s35]) ).
cnf(s39,plain,
spl413_19,
inference(rat,[],[s14,s30,s37]) ).
cnf(s41,plain,
~ spl413_17,
inference(rat,[],[s29,s35,s39]) ).
cnf(s42,plain,
~ spl413_16,
inference(rat,[],[s27,s35,s39]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s13,s30,s41,s42]) ).
fof(f6647,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT169+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.40 % Computer : n010.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.41 % CPULimit : 300
% 0.12/5.41 % WCLimit : 300
% 0.12/5.41 % DateTime : Sun Sep 27 23:54:22 UTC 2026
% 0.12/5.41 % CPUTime :
% 0.12/5.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.44 Running first-order theorem proving
% 0.12/5.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.50/7.94 % (1435873)Detected formulas, will run a generic FOF schedule.
% 13.50/7.94 % (1435879)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2968517134:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 13.50/7.94 % (1435883)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=997899919:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 13.50/7.94 % (1435884)dis-21_1_sil=8000:lcm=predicate:random_seed=1439086799:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 13.50/7.94 % (1435882)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2096880577:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 13.50/7.94 % (1435881)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1368964488:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 13.50/7.94 % (1435878)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2676629119:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 13.50/7.94 % (1435880)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3317627833:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 13.50/7.94 % (1435881)Refutation not found, incomplete strategy
% 13.50/7.94 % (1435881)------------------------------
% 13.50/7.94 % (1435881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.50/7.94 % (1435881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.50/7.94 % (1435881)CaDiCaL version: 2.1.3
% 13.50/7.94 % (1435881)Termination reason: Refutation not found, incomplete strategy
% 13.50/7.94 % (1435881)Time elapsed: 0.009 s
% 13.50/7.94 % (1435881)Peak memory usage: 90 MB
% 13.50/7.94 % (1435881)Instructions burned: 12 (million)
% 13.50/7.94 % (1435884)Instruction limit reached!
% 13.50/7.94 % (1435884)------------------------------
% 13.50/7.94 % (1435884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.50/7.94 % (1435884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.50/7.94 % (1435884)CaDiCaL version: 2.1.3
% 13.50/7.94 % (1435884)Termination reason: Instruction limit
% 13.50/7.94 % (1435884)Termination phase: Property scanning
% 13.50/7.94 % (1435884)Time elapsed: 0.059 s
% 13.50/7.94 % (1435884)Peak memory usage: 89 MB
% 13.50/7.94 % (1435884)Instructions burned: 131 (million)
% 13.50/7.94 % (1435883)Instruction limit reached!
% 13.50/7.94 % (1435883)------------------------------
% 13.50/7.94 % (1435883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.50/7.94 % (1435883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.50/7.94 % (1435883)CaDiCaL version: 2.1.3
% 13.50/7.94 % (1435883)Termination reason: Instruction limit
% 13.50/7.94 % (1435883)Termination phase: Saturation
% 13.50/7.94 % (1435883)Time elapsed: 0.066 s
% 13.50/7.94 % (1435883)Peak memory usage: 90 MB
% 13.50/7.94 % (1435883)Instructions burned: 139 (million)
% 13.50/7.94 % (1435882)Instruction limit reached!
% 13.50/7.94 % (1435882)------------------------------
% 13.50/7.94 % (1435882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.50/7.94 % (1435882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.50/7.94 % (1435882)CaDiCaL version: 2.1.3
% 13.50/7.94 % (1435882)Termination reason: Instruction limit
% 13.50/7.94 % (1435882)Termination phase: Saturation
% 13.50/7.94 % (1435882)Time elapsed: 0.069 s
% 13.50/7.94 % (1435882)Peak memory usage: 90 MB
% 13.50/7.94 % (1435882)Instructions burned: 120 (million)
% 13.50/7.94 % (1435893)lrs+10_1_sil=32000:urr=on:br=off:random_seed=811773744:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 13.50/7.94 % (1435892)lrs+10_1_sil=8000:sp=occurrence:random_seed=4277282667:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 13.50/7.94 % (1435894)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3958928450:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 13.50/7.94 % (1435881)------------------------------
% 13.50/7.94 % (1435881)------------------------------
% 13.50/7.94 % (1435893)Instruction limit reached!
% 13.50/7.94 % (1435893)------------------------------
% 13.50/7.94 % (1435893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435893)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435893)Termination reason: Instruction limit
% 15.24/8.13 % (1435893)Termination phase: Saturation
% 15.24/8.13 % (1435893)Time elapsed: 0.088 s
% 15.24/8.13 % (1435893)Peak memory usage: 91 MB
% 15.24/8.13 % (1435893)Instructions burned: 157 (million)
% 15.24/8.13 % (1435892)Instruction limit reached!
% 15.24/8.13 % (1435892)------------------------------
% 15.24/8.13 % (1435892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435892)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435892)Termination reason: Instruction limit
% 15.24/8.13 % (1435892)Termination phase: Saturation
% 15.24/8.13 % (1435892)Time elapsed: 0.172 s
% 15.24/8.13 % (1435892)Peak memory usage: 92 MB
% 15.24/8.13 % (1435892)Instructions burned: 285 (million)
% 15.24/8.13 % (1435898)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3217735463:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 15.24/8.13 % (1435894)Instruction limit reached!
% 15.24/8.13 % (1435894)------------------------------
% 15.24/8.13 % (1435894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435894)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435894)Termination reason: Instruction limit
% 15.24/8.13 % (1435894)Termination phase: Saturation
% 15.24/8.13 % (1435894)Time elapsed: 0.192 s
% 15.24/8.13 % (1435894)Peak memory usage: 93 MB
% 15.24/8.13 % (1435894)Instructions burned: 326 (million)
% 15.24/8.13 % (1435899)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2487836827:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 15.24/8.13 % (1435899)Refutation not found, incomplete strategy
% 15.24/8.13 % (1435899)------------------------------
% 15.24/8.13 % (1435899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435899)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435899)Termination reason: Refutation not found, incomplete strategy
% 15.24/8.13 % (1435899)Time elapsed: 0.058 s
% 15.24/8.13 % (1435899)Peak memory usage: 91 MB
% 15.24/8.13 % (1435899)Instructions burned: 106 (million)
% 15.24/8.13 % (1435900)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1842412269:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 15.24/8.13 % (1435898)Instruction limit reached!
% 15.24/8.13 % (1435898)------------------------------
% 15.24/8.13 % (1435898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435898)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435898)Termination reason: Instruction limit
% 15.24/8.13 % (1435898)Termination phase: Saturation
% 15.24/8.13 % (1435898)Time elapsed: 0.143 s
% 15.24/8.13 % (1435898)Peak memory usage: 93 MB
% 15.24/8.13 % (1435898)Instructions burned: 250 (million)
% 15.24/8.13 % (1435903)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4252292329:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 15.24/8.13 % (1435903)Instruction limit reached!
% 15.24/8.13 % (1435903)------------------------------
% 15.24/8.13 % (1435903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435903)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435903)Termination reason: Instruction limit
% 15.24/8.13 % (1435903)Termination phase: Saturation
% 15.24/8.13 % (1435903)Time elapsed: 0.056 s
% 15.24/8.13 % (1435903)Peak memory usage: 90 MB
% 15.24/8.13 % (1435903)Instructions burned: 114 (million)
% 15.24/8.13 % (1435906)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4188609343:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 15.24/8.13 % (1435899)------------------------------
% 15.24/8.13 % (1435899)------------------------------
% 15.24/8.13 % (1435907)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=657349893:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 15.24/8.13 % (1435906)Instruction limit reached!
% 15.24/8.13 % (1435906)------------------------------
% 15.24/8.13 % (1435906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435906)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435906)Termination reason: Instruction limit
% 15.24/8.13 % (1435906)Termination phase: Property scanning
% 15.24/8.13 % (1435906)Time elapsed: 0.061 s
% 15.24/8.13 % (1435906)Peak memory usage: 89 MB
% 15.24/8.13 % (1435906)Instructions burned: 129 (million)
% 15.24/8.13 % (1435907)Instruction limit reached!
% 15.24/8.13 % (1435907)------------------------------
% 15.24/8.13 % (1435907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435907)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435907)Termination reason: Instruction limit
% 15.24/8.13 % (1435907)Termination phase: Saturation
% 15.24/8.13 % (1435907)Time elapsed: 0.054 s
% 15.24/8.13 % (1435907)Peak memory usage: 90 MB
% 15.24/8.13 % (1435907)Instructions burned: 115 (million)
% 15.24/8.13 % (1435909)lrs+10_1_sil=8000:sp=occurrence:random_seed=25932372:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 15.24/8.13 % (1435911)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3605488548:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 15.24/8.13 % (1435912)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1866033430:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 15.24/8.13 % (1435911)Refutation not found, incomplete strategy
% 15.24/8.13 % (1435911)------------------------------
% 15.24/8.13 % (1435911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435911)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435911)Termination reason: Refutation not found, incomplete strategy
% 15.24/8.13 % (1435911)Time elapsed: 0.100 s
% 15.24/8.13 % (1435911)Peak memory usage: 93 MB
% 15.24/8.13 % (1435911)Instructions burned: 194 (million)
% 15.24/8.13 % (1435911)------------------------------
% 15.24/8.13 % (1435911)------------------------------
% 15.24/8.13 % (1435916)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3899937781:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2985 on theBenchmark for (2985ds/134Mi)
% 15.24/8.13 % (1435909)Instruction limit reached!
% 15.24/8.13 % (1435909)------------------------------
% 15.24/8.13 % (1435909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435909)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435909)Termination reason: Instruction limit
% 15.24/8.13 % (1435909)Termination phase: Saturation
% 15.24/8.13 % (1435909)Time elapsed: 0.547 s
% 15.24/8.13 % (1435909)Peak memory usage: 97 MB
% 15.24/8.13 % (1435909)Instructions burned: 908 (million)
% 15.24/8.13 % (1435916)Instruction limit reached!
% 15.24/8.13 % (1435916)------------------------------
% 15.24/8.13 % (1435916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435916)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435916)Termination reason: Instruction limit
% 15.24/8.13 % (1435916)Termination phase: Saturation
% 15.24/8.13 % (1435916)Time elapsed: 0.067 s
% 15.24/8.13 % (1435916)Peak memory usage: 91 MB
% 15.24/8.13 % (1435916)Instructions burned: 136 (million)
% 15.24/8.13 % (1435918)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4059591175:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 15.24/8.13 % (1435919)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2198076205:st=3:i=13193:sd=3:ss=axioms_2983 on theBenchmark for (2983ds/13193Mi)
% 15.24/8.13 % (1435900)First to succeed.
% 15.24/8.13 % (1435900)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1435873"
% 15.24/8.13 % (1435918)Instruction limit reached!
% 15.24/8.13 % (1435918)------------------------------
% 15.24/8.13 % (1435918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.24/8.13 % (1435918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.24/8.13 % (1435918)CaDiCaL version: 2.1.3
% 15.24/8.13 % (1435918)Termination reason: Instruction limit
% 15.24/8.13 % (1435918)Termination phase: Saturation
% 15.24/8.13 % (1435918)Time elapsed: 0.329 s
% 15.24/8.13 % (1435918)Peak memory usage: 100 MB
% 15.24/8.13 % (1435918)Instructions burned: 592 (million)
% 15.24/8.13 % (1435922)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=970886472:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2979 on theBenchmark for (2979ds/125Mi)
% 15.24/8.13 % (1435900)Refutation found. Thanks to Tanya!
% 15.24/8.13 % SZS status Theorem for theBenchmark
% 15.24/8.13 % SZS output start Proof for theBenchmark
% See solution above
% 16.03/8.23 % (1435900)------------------------------
% 16.03/8.23 % (1435900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.03/8.23 % (1435900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.03/8.23 % (1435900)CaDiCaL version: 2.1.3
% 16.03/8.23 % (1435900)Termination reason: Refutation
% 16.03/8.23 % (1435900)Time elapsed: 1.277 s
% 16.03/8.23 % (1435900)Peak memory usage: 164 MB
% 16.03/8.23 % (1435900)Instructions burned: 2165 (million)
% 16.03/8.23 % (1435900)------------------------------
% 16.03/8.23 % (1435900)------------------------------
% 16.03/8.23 % (1435873)Success in time 2.251 s
% 16.03/8.23 % Vampire exiting
%------------------------------------------------------------------------------