TSTP Solution File: SWW672_2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWW672_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n006.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 : 300s
% DateTime : Tue May 21 07:02:12 EDT 2024
% Result : Theorem 0.58s 0.78s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 94
% Syntax : Number of formulae : 140 ( 14 unt; 79 typ; 0 def)
% Number of atoms : 638 ( 215 equ)
% Maximal formula atoms : 60 ( 10 avg)
% Number of connectives : 779 ( 202 ~; 123 |; 352 &)
% ( 17 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 110 ( 12 atm; 26 fun; 38 num; 34 var)
% Number of types : 8 ( 6 usr; 1 ari)
% Number of type conns : 114 ( 48 >; 66 *; 0 +; 0 <<)
% Number of predicates : 20 ( 16 usr; 1 prp; 0-6 aty)
% Number of functors : 60 ( 57 usr; 27 con; 0-4 aty)
% Number of variables : 387 ( 203 !; 184 ?; 387 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool1: $tType ).
tff(type_def_8,type,
tuple02: $tType ).
tff(type_def_9,type,
vertex1: $tType ).
tff(type_def_10,type,
set_vertex: $tType ).
tff(func_def_0,type,
witness1: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool: ty ).
tff(func_def_4,type,
true1: bool1 ).
tff(func_def_5,type,
false1: bool1 ).
tff(func_def_6,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(func_def_7,type,
tuple0: ty ).
tff(func_def_8,type,
tuple03: tuple02 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
set: ty > ty ).
tff(func_def_13,type,
empty: ty > uni ).
tff(func_def_14,type,
add: ( ty * uni * uni ) > uni ).
tff(func_def_15,type,
remove: ( ty * uni * uni ) > uni ).
tff(func_def_16,type,
union: ( ty * uni * uni ) > uni ).
tff(func_def_17,type,
inter: ( ty * uni * uni ) > uni ).
tff(func_def_18,type,
diff: ( ty * uni * uni ) > uni ).
tff(func_def_19,type,
choose: ( ty * uni ) > uni ).
tff(func_def_20,type,
cardinal1: ( ty * uni ) > $int ).
tff(func_def_23,type,
vertex: ty ).
tff(func_def_24,type,
succ1: vertex1 > set_vertex ).
tff(func_def_25,type,
t2tb: set_vertex > uni ).
tff(func_def_26,type,
tb2t: uni > set_vertex ).
tff(func_def_27,type,
t2tb1: vertex1 > uni ).
tff(func_def_28,type,
tb2t1: uni > vertex1 ).
tff(func_def_29,type,
ref: ty > ty ).
tff(func_def_30,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_31,type,
contents: ( ty * uni ) > uni ).
tff(func_def_33,type,
sK2: vertex1 ).
tff(func_def_34,type,
sK3: vertex1 ).
tff(func_def_35,type,
sK4: $int ).
tff(func_def_36,type,
sK5: set_vertex ).
tff(func_def_37,type,
sK6: set_vertex ).
tff(func_def_38,type,
sK7: set_vertex ).
tff(func_def_39,type,
sK8: bool1 ).
tff(func_def_40,type,
sK9: set_vertex ).
tff(func_def_41,type,
sK10: vertex1 ).
tff(func_def_42,type,
sK11: set_vertex ).
tff(func_def_43,type,
sK12: set_vertex ).
tff(func_def_44,type,
sK13: bool1 ).
tff(func_def_45,type,
sK14: set_vertex ).
tff(func_def_46,type,
sK15: set_vertex ).
tff(func_def_47,type,
sK16: $int ).
tff(func_def_48,type,
sK17: vertex1 ).
tff(func_def_49,type,
sK18: ( ty * uni * uni ) > uni ).
tff(func_def_50,type,
sK19: ( ty * uni ) > uni ).
tff(func_def_51,type,
sK20: ( vertex1 * vertex1 * $int ) > $int ).
tff(func_def_52,type,
sK21: ( $int * vertex1 * vertex1 ) > $int ).
tff(func_def_53,type,
sK22: ( set_vertex * vertex1 ) > vertex1 ).
tff(func_def_54,type,
sK23: set_vertex > vertex1 ).
tff(func_def_55,type,
sK24: set_vertex > vertex1 ).
tff(func_def_56,type,
sK25: ( vertex1 * vertex1 * $int ) > vertex1 ).
tff(func_def_57,type,
sK26: ( $int * vertex1 * vertex1 ) > vertex1 ).
tff(func_def_58,type,
sK27: ( $int * vertex1 * vertex1 ) > vertex1 ).
tff(func_def_59,type,
sK28: ( $int * vertex1 * vertex1 ) > vertex1 ).
tff(func_def_60,type,
sK29: ( $int * vertex1 * vertex1 ) > $int ).
tff(func_def_61,type,
sK30: ( vertex1 * vertex1 * $int ) > vertex1 ).
tff(pred_def_1,type,
sort1: ( ty * uni ) > $o ).
tff(pred_def_3,type,
mem: ( ty * uni * uni ) > $o ).
tff(pred_def_4,type,
infix_eqeq: ( ty * uni * uni ) > $o ).
tff(pred_def_5,type,
subset: ( ty * uni * uni ) > $o ).
tff(pred_def_6,type,
is_empty: ( ty * uni ) > $o ).
tff(pred_def_7,type,
path1: ( vertex1 * vertex1 * $int ) > $o ).
tff(pred_def_8,type,
shortest_path1: ( vertex1 * vertex1 * $int ) > $o ).
tff(pred_def_10,type,
inv1: ( vertex1 * vertex1 * set_vertex * set_vertex * set_vertex * $int ) > $o ).
tff(pred_def_11,type,
closure1: ( set_vertex * set_vertex * set_vertex * vertex1 ) > $o ).
tff(pred_def_12,type,
sP0: ( $int * vertex1 * set_vertex ) > $o ).
tff(pred_def_13,type,
sP1: ( $int * vertex1 * vertex1 ) > $o ).
tff(pred_def_14,type,
sQ31_eqProxy: ( $int * $int ) > $o ).
tff(pred_def_15,type,
sQ32_eqProxy: ( set_vertex * set_vertex ) > $o ).
tff(pred_def_16,type,
sQ33_eqProxy: ( bool1 * bool1 ) > $o ).
tff(pred_def_17,type,
sQ34_eqProxy: ( vertex1 * vertex1 ) > $o ).
tff(pred_def_18,type,
sQ35_eqProxy: ( uni * uni ) > $o ).
tff(f605,plain,
$false,
inference(subsumption_resolution,[],[f604,f338]) ).
tff(f338,plain,
mem(vertex,t2tb1(sK22(sK12,sK17)),t2tb(succ1(sK17))),
inference(resolution,[],[f214,f244]) ).
tff(f244,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex] :
( closure1(X0,X1,X2,X3)
| mem(vertex,t2tb1(sK22(X0,X3)),t2tb(succ1(X3))) ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: set_vertex,X1: set_vertex,X2: set_vertex,X3: vertex1] :
( ( closure1(X0,X1,X2,X3)
| ( ~ mem(vertex,t2tb1(sK22(X0,X3)),t2tb(X0))
& mem(vertex,t2tb1(sK22(X0,X3)),t2tb(succ1(X3)))
& ~ mem(vertex,t2tb1(X3),t2tb(X2))
& ~ mem(vertex,t2tb1(X3),t2tb(X1))
& mem(vertex,t2tb1(X3),t2tb(X0)) ) )
& ( ! [X5: vertex1] :
( mem(vertex,t2tb1(X5),t2tb(X0))
| ~ mem(vertex,t2tb1(X5),t2tb(succ1(X3))) )
| mem(vertex,t2tb1(X3),t2tb(X2))
| mem(vertex,t2tb1(X3),t2tb(X1))
| ~ mem(vertex,t2tb1(X3),t2tb(X0))
| ~ closure1(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f173,f174]) ).
tff(f174,plain,
! [X0: set_vertex,X3: vertex1] :
( ? [X4: vertex1] :
( ~ mem(vertex,t2tb1(X4),t2tb(X0))
& mem(vertex,t2tb1(X4),t2tb(succ1(X3))) )
=> ( ~ mem(vertex,t2tb1(sK22(X0,X3)),t2tb(X0))
& mem(vertex,t2tb1(sK22(X0,X3)),t2tb(succ1(X3))) ) ),
introduced(choice_axiom,[]) ).
tff(f173,plain,
! [X0: set_vertex,X1: set_vertex,X2: set_vertex,X3: vertex1] :
( ( closure1(X0,X1,X2,X3)
| ( ? [X4: vertex1] :
( ~ mem(vertex,t2tb1(X4),t2tb(X0))
& mem(vertex,t2tb1(X4),t2tb(succ1(X3))) )
& ~ mem(vertex,t2tb1(X3),t2tb(X2))
& ~ mem(vertex,t2tb1(X3),t2tb(X1))
& mem(vertex,t2tb1(X3),t2tb(X0)) ) )
& ( ! [X5: vertex1] :
( mem(vertex,t2tb1(X5),t2tb(X0))
| ~ mem(vertex,t2tb1(X5),t2tb(succ1(X3))) )
| mem(vertex,t2tb1(X3),t2tb(X2))
| mem(vertex,t2tb1(X3),t2tb(X1))
| ~ mem(vertex,t2tb1(X3),t2tb(X0))
| ~ closure1(X0,X1,X2,X3) ) ),
inference(rectify,[],[f172]) ).
tff(f172,plain,
! [X0: set_vertex,X1: set_vertex,X2: set_vertex,X3: vertex1] :
( ( closure1(X0,X1,X2,X3)
| ( ? [X4: vertex1] :
( ~ mem(vertex,t2tb1(X4),t2tb(X0))
& mem(vertex,t2tb1(X4),t2tb(succ1(X3))) )
& ~ mem(vertex,t2tb1(X3),t2tb(X2))
& ~ mem(vertex,t2tb1(X3),t2tb(X1))
& mem(vertex,t2tb1(X3),t2tb(X0)) ) )
& ( ! [X4: vertex1] :
( mem(vertex,t2tb1(X4),t2tb(X0))
| ~ mem(vertex,t2tb1(X4),t2tb(succ1(X3))) )
| mem(vertex,t2tb1(X3),t2tb(X2))
| mem(vertex,t2tb1(X3),t2tb(X1))
| ~ mem(vertex,t2tb1(X3),t2tb(X0))
| ~ closure1(X0,X1,X2,X3) ) ),
inference(flattening,[],[f171]) ).
tff(f171,plain,
! [X0: set_vertex,X1: set_vertex,X2: set_vertex,X3: vertex1] :
( ( closure1(X0,X1,X2,X3)
| ( ? [X4: vertex1] :
( ~ mem(vertex,t2tb1(X4),t2tb(X0))
& mem(vertex,t2tb1(X4),t2tb(succ1(X3))) )
& ~ mem(vertex,t2tb1(X3),t2tb(X2))
& ~ mem(vertex,t2tb1(X3),t2tb(X1))
& mem(vertex,t2tb1(X3),t2tb(X0)) ) )
& ( ! [X4: vertex1] :
( mem(vertex,t2tb1(X4),t2tb(X0))
| ~ mem(vertex,t2tb1(X4),t2tb(succ1(X3))) )
| mem(vertex,t2tb1(X3),t2tb(X2))
| mem(vertex,t2tb1(X3),t2tb(X1))
| ~ mem(vertex,t2tb1(X3),t2tb(X0))
| ~ closure1(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: set_vertex,X1: set_vertex,X2: set_vertex,X3: vertex1] :
( closure1(X0,X1,X2,X3)
<=> ( ! [X4: vertex1] :
( mem(vertex,t2tb1(X4),t2tb(X0))
| ~ mem(vertex,t2tb1(X4),t2tb(succ1(X3))) )
| mem(vertex,t2tb1(X3),t2tb(X2))
| mem(vertex,t2tb1(X3),t2tb(X1))
| ~ mem(vertex,t2tb1(X3),t2tb(X0)) ) ),
inference(flattening,[],[f123]) ).
tff(f123,plain,
! [X0: set_vertex,X1: set_vertex,X2: set_vertex,X3: vertex1] :
( closure1(X0,X1,X2,X3)
<=> ( ! [X4: vertex1] :
( mem(vertex,t2tb1(X4),t2tb(X0))
| ~ mem(vertex,t2tb1(X4),t2tb(succ1(X3))) )
| mem(vertex,t2tb1(X3),t2tb(X2))
| mem(vertex,t2tb1(X3),t2tb(X1))
| ~ mem(vertex,t2tb1(X3),t2tb(X0)) ) ),
inference(ennf_transformation,[],[f94]) ).
tff(f94,plain,
! [X0: set_vertex,X1: set_vertex,X2: set_vertex,X3: vertex1] :
( closure1(X0,X1,X2,X3)
<=> ( mem(vertex,t2tb1(X3),t2tb(X0))
=> ( ~ mem(vertex,t2tb1(X3),t2tb(X1))
=> ( ~ mem(vertex,t2tb1(X3),t2tb(X2))
=> ! [X4: vertex1] :
( mem(vertex,t2tb1(X4),t2tb(succ1(X3)))
=> mem(vertex,t2tb1(X4),t2tb(X0)) ) ) ) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X22: set_vertex,X23: set_vertex,X24: set_vertex,X1: vertex1] :
( closure1(X22,X23,X24,X1)
<=> ( mem(vertex,t2tb1(X1),t2tb(X22))
=> ( ~ mem(vertex,t2tb1(X1),t2tb(X23))
=> ( ~ mem(vertex,t2tb1(X1),t2tb(X24))
=> ! [X7: vertex1] :
( mem(vertex,t2tb1(X7),t2tb(succ1(X1)))
=> mem(vertex,t2tb1(X7),t2tb(X22)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_def) ).
tff(f214,plain,
~ closure1(sK12,sK14,sK15,sK17),
inference(cnf_transformation,[],[f155]) ).
tff(f155,plain,
( ~ closure1(sK12,sK14,sK15,sK17)
& ( $sum(sK4,1) = sK16 )
& ( tb2t(empty(vertex)) = sK15 )
& ( sK11 = sK14 )
& ( true1 = sK13 )
& ( ( true1 = sK13 )
| ~ is_empty(vertex,t2tb(sK9)) )
& ( is_empty(vertex,t2tb(sK9))
| ( true1 != sK13 ) )
& ! [X16: vertex1] : closure1(sK12,sK9,sK11,X16)
& subset(vertex,t2tb(succ1(sK10)),t2tb(sK12))
& inv1(sK2,sK3,sK12,sK9,sK11,sK4)
& ! [X17: vertex1] :
( closure1(sK7,sK9,sK5,X17)
| ( sK10 = X17 ) )
& shortest_path1(sK2,sK10,sK4)
& inv1(sK2,sK3,sK7,sK9,sK5,sK4)
& ( sK3 != sK10 )
& ( sK9 = tb2t(remove(vertex,t2tb1(sK10),t2tb(sK6))) )
& mem(vertex,t2tb1(sK10),t2tb(sK6))
& ~ is_empty(vertex,t2tb(sK6))
& ( true1 != sK8 )
& ( ( true1 = sK8 )
| ~ is_empty(vertex,t2tb(sK6)) )
& ( is_empty(vertex,t2tb(sK6))
| ( true1 != sK8 ) )
& ~ $less(sK4,0)
& ! [X18: vertex1] : closure1(sK7,sK6,sK5,X18)
& ( is_empty(vertex,t2tb(sK5))
| ~ is_empty(vertex,t2tb(sK6)) )
& inv1(sK2,sK3,sK7,sK6,sK5,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17])],[f145,f154,f153,f152,f151,f150,f149,f148,f147,f146]) ).
tff(f146,plain,
( ? [X0: vertex1,X1: vertex1,X2: $int,X3: set_vertex,X4: set_vertex,X5: set_vertex] :
( ? [X6: bool1] :
( ? [X7: set_vertex,X8: vertex1] :
( ? [X9: set_vertex,X10: set_vertex] :
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(X10,X12,X13,X15)
& ( $sum(X2,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(X7)) )
& ( is_empty(vertex,t2tb(X7))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,X7,X9,X16)
& subset(vertex,t2tb(succ1(X8)),t2tb(X10))
& inv1(X0,X1,X10,X7,X9,X2) )
& ! [X17: vertex1] :
( closure1(X5,X7,X3,X17)
| ( X8 = X17 ) )
& shortest_path1(X0,X8,X2)
& inv1(X0,X1,X5,X7,X3,X2)
& ( X1 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(X4))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(X4)) )
& ~ is_empty(vertex,t2tb(X4))
& ( true1 != X6 )
& ( ( true1 = X6 )
| ~ is_empty(vertex,t2tb(X4)) )
& ( is_empty(vertex,t2tb(X4))
| ( true1 != X6 ) ) )
& ~ $less(X2,0)
& ! [X18: vertex1] : closure1(X5,X4,X3,X18)
& ( is_empty(vertex,t2tb(X3))
| ~ is_empty(vertex,t2tb(X4)) )
& inv1(X0,X1,X5,X4,X3,X2) )
=> ( ? [X6: bool1] :
( ? [X8: vertex1,X7: set_vertex] :
( ? [X10: set_vertex,X9: set_vertex] :
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(X10,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(X7)) )
& ( is_empty(vertex,t2tb(X7))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,X7,X9,X16)
& subset(vertex,t2tb(succ1(X8)),t2tb(X10))
& inv1(sK2,sK3,X10,X7,X9,sK4) )
& ! [X17: vertex1] :
( closure1(sK7,X7,sK5,X17)
| ( X8 = X17 ) )
& shortest_path1(sK2,X8,sK4)
& inv1(sK2,sK3,sK7,X7,sK5,sK4)
& ( sK3 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(sK6))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(sK6)) )
& ~ is_empty(vertex,t2tb(sK6))
& ( true1 != X6 )
& ( ( true1 = X6 )
| ~ is_empty(vertex,t2tb(sK6)) )
& ( is_empty(vertex,t2tb(sK6))
| ( true1 != X6 ) ) )
& ~ $less(sK4,0)
& ! [X18: vertex1] : closure1(sK7,sK6,sK5,X18)
& ( is_empty(vertex,t2tb(sK5))
| ~ is_empty(vertex,t2tb(sK6)) )
& inv1(sK2,sK3,sK7,sK6,sK5,sK4) ) ),
introduced(choice_axiom,[]) ).
tff(f147,plain,
( ? [X6: bool1] :
( ? [X8: vertex1,X7: set_vertex] :
( ? [X10: set_vertex,X9: set_vertex] :
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(X10,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(X7)) )
& ( is_empty(vertex,t2tb(X7))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,X7,X9,X16)
& subset(vertex,t2tb(succ1(X8)),t2tb(X10))
& inv1(sK2,sK3,X10,X7,X9,sK4) )
& ! [X17: vertex1] :
( closure1(sK7,X7,sK5,X17)
| ( X8 = X17 ) )
& shortest_path1(sK2,X8,sK4)
& inv1(sK2,sK3,sK7,X7,sK5,sK4)
& ( sK3 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(sK6))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(sK6)) )
& ~ is_empty(vertex,t2tb(sK6))
& ( true1 != X6 )
& ( ( true1 = X6 )
| ~ is_empty(vertex,t2tb(sK6)) )
& ( is_empty(vertex,t2tb(sK6))
| ( true1 != X6 ) ) )
=> ( ? [X8: vertex1,X7: set_vertex] :
( ? [X10: set_vertex,X9: set_vertex] :
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(X10,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(X7)) )
& ( is_empty(vertex,t2tb(X7))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,X7,X9,X16)
& subset(vertex,t2tb(succ1(X8)),t2tb(X10))
& inv1(sK2,sK3,X10,X7,X9,sK4) )
& ! [X17: vertex1] :
( closure1(sK7,X7,sK5,X17)
| ( X8 = X17 ) )
& shortest_path1(sK2,X8,sK4)
& inv1(sK2,sK3,sK7,X7,sK5,sK4)
& ( sK3 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(sK6))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(sK6)) )
& ~ is_empty(vertex,t2tb(sK6))
& ( true1 != sK8 )
& ( ( true1 = sK8 )
| ~ is_empty(vertex,t2tb(sK6)) )
& ( is_empty(vertex,t2tb(sK6))
| ( true1 != sK8 ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f148,plain,
( ? [X8: vertex1,X7: set_vertex] :
( ? [X10: set_vertex,X9: set_vertex] :
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(X10,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(X7)) )
& ( is_empty(vertex,t2tb(X7))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,X7,X9,X16)
& subset(vertex,t2tb(succ1(X8)),t2tb(X10))
& inv1(sK2,sK3,X10,X7,X9,sK4) )
& ! [X17: vertex1] :
( closure1(sK7,X7,sK5,X17)
| ( X8 = X17 ) )
& shortest_path1(sK2,X8,sK4)
& inv1(sK2,sK3,sK7,X7,sK5,sK4)
& ( sK3 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(sK6))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(sK6)) )
=> ( ? [X10: set_vertex,X9: set_vertex] :
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(X10,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(sK9)) )
& ( is_empty(vertex,t2tb(sK9))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,sK9,X9,X16)
& subset(vertex,t2tb(succ1(sK10)),t2tb(X10))
& inv1(sK2,sK3,X10,sK9,X9,sK4) )
& ! [X17: vertex1] :
( closure1(sK7,sK9,sK5,X17)
| ( sK10 = X17 ) )
& shortest_path1(sK2,sK10,sK4)
& inv1(sK2,sK3,sK7,sK9,sK5,sK4)
& ( sK3 != sK10 )
& ( sK9 = tb2t(remove(vertex,t2tb1(sK10),t2tb(sK6))) )
& mem(vertex,t2tb1(sK10),t2tb(sK6)) ) ),
introduced(choice_axiom,[]) ).
tff(f149,plain,
( ? [X10: set_vertex,X9: set_vertex] :
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(X10,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(sK9)) )
& ( is_empty(vertex,t2tb(sK9))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,sK9,X9,X16)
& subset(vertex,t2tb(succ1(sK10)),t2tb(X10))
& inv1(sK2,sK3,X10,sK9,X9,sK4) )
=> ( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK12,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK11 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(sK9)) )
& ( is_empty(vertex,t2tb(sK9))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(sK12,sK9,sK11,X16)
& subset(vertex,t2tb(succ1(sK10)),t2tb(sK12))
& inv1(sK2,sK3,sK12,sK9,sK11,sK4) ) ),
introduced(choice_axiom,[]) ).
tff(f150,plain,
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK12,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK11 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(sK9)) )
& ( is_empty(vertex,t2tb(sK9))
| ( true1 != X11 ) ) )
=> ( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK12,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK11 = X12 ) )
& ( true1 = sK13 )
& ( ( true1 = sK13 )
| ~ is_empty(vertex,t2tb(sK9)) )
& ( is_empty(vertex,t2tb(sK9))
| ( true1 != sK13 ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f151,plain,
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK12,X12,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK11 = X12 ) )
=> ( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK12,sK14,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK11 = sK14 ) ) ),
introduced(choice_axiom,[]) ).
tff(f152,plain,
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK12,sK14,X13,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
=> ( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK12,sK14,sK15,X15)
& ( $sum(sK4,1) = X14 ) )
& ( tb2t(empty(vertex)) = sK15 ) ) ),
introduced(choice_axiom,[]) ).
tff(f153,plain,
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK12,sK14,sK15,X15)
& ( $sum(sK4,1) = X14 ) )
=> ( ? [X15: vertex1] : ~ closure1(sK12,sK14,sK15,X15)
& ( $sum(sK4,1) = sK16 ) ) ),
introduced(choice_axiom,[]) ).
tff(f154,plain,
( ? [X15: vertex1] : ~ closure1(sK12,sK14,sK15,X15)
=> ~ closure1(sK12,sK14,sK15,sK17) ),
introduced(choice_axiom,[]) ).
tff(f145,plain,
? [X0: vertex1,X1: vertex1,X2: $int,X3: set_vertex,X4: set_vertex,X5: set_vertex] :
( ? [X6: bool1] :
( ? [X7: set_vertex,X8: vertex1] :
( ? [X9: set_vertex,X10: set_vertex] :
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(X10,X12,X13,X15)
& ( $sum(X2,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(X7)) )
& ( is_empty(vertex,t2tb(X7))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,X7,X9,X16)
& subset(vertex,t2tb(succ1(X8)),t2tb(X10))
& inv1(X0,X1,X10,X7,X9,X2) )
& ! [X17: vertex1] :
( closure1(X5,X7,X3,X17)
| ( X8 = X17 ) )
& shortest_path1(X0,X8,X2)
& inv1(X0,X1,X5,X7,X3,X2)
& ( X1 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(X4))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(X4)) )
& ~ is_empty(vertex,t2tb(X4))
& ( true1 != X6 )
& ( ( true1 = X6 )
| ~ is_empty(vertex,t2tb(X4)) )
& ( is_empty(vertex,t2tb(X4))
| ( true1 != X6 ) ) )
& ~ $less(X2,0)
& ! [X18: vertex1] : closure1(X5,X4,X3,X18)
& ( is_empty(vertex,t2tb(X3))
| ~ is_empty(vertex,t2tb(X4)) )
& inv1(X0,X1,X5,X4,X3,X2) ),
inference(rectify,[],[f144]) ).
tff(f144,plain,
? [X0: vertex1,X1: vertex1,X2: $int,X3: set_vertex,X4: set_vertex,X5: set_vertex] :
( ? [X7: bool1] :
( ? [X8: set_vertex,X9: vertex1] :
( ? [X11: set_vertex,X12: set_vertex] :
( ? [X14: bool1] :
( ? [X15: set_vertex] :
( ? [X16: set_vertex] :
( ? [X17: $int] :
( ? [X18: vertex1] : ~ closure1(X12,X15,X16,X18)
& ( $sum(X2,1) = X17 ) )
& ( tb2t(empty(vertex)) = X16 ) )
& ( X11 = X15 ) )
& ( true1 = X14 )
& ( ( true1 = X14 )
| ~ is_empty(vertex,t2tb(X8)) )
& ( is_empty(vertex,t2tb(X8))
| ( true1 != X14 ) ) )
& ! [X13: vertex1] : closure1(X12,X8,X11,X13)
& subset(vertex,t2tb(succ1(X9)),t2tb(X12))
& inv1(X0,X1,X12,X8,X11,X2) )
& ! [X10: vertex1] :
( closure1(X5,X8,X3,X10)
| ( X9 = X10 ) )
& shortest_path1(X0,X9,X2)
& inv1(X0,X1,X5,X8,X3,X2)
& ( X1 != X9 )
& ( tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 )
& mem(vertex,t2tb1(X9),t2tb(X4)) )
& ~ is_empty(vertex,t2tb(X4))
& ( true1 != X7 )
& ( ( true1 = X7 )
| ~ is_empty(vertex,t2tb(X4)) )
& ( is_empty(vertex,t2tb(X4))
| ( true1 != X7 ) ) )
& ~ $less(X2,0)
& ! [X6: vertex1] : closure1(X5,X4,X3,X6)
& ( is_empty(vertex,t2tb(X3))
| ~ is_empty(vertex,t2tb(X4)) )
& inv1(X0,X1,X5,X4,X3,X2) ),
inference(flattening,[],[f143]) ).
tff(f143,plain,
? [X0: vertex1,X1: vertex1,X2: $int,X3: set_vertex,X4: set_vertex,X5: set_vertex] :
( ? [X7: bool1] :
( ? [X8: set_vertex,X9: vertex1] :
( ? [X11: set_vertex,X12: set_vertex] :
( ? [X14: bool1] :
( ? [X15: set_vertex] :
( ? [X16: set_vertex] :
( ? [X17: $int] :
( ? [X18: vertex1] : ~ closure1(X12,X15,X16,X18)
& ( $sum(X2,1) = X17 ) )
& ( tb2t(empty(vertex)) = X16 ) )
& ( X11 = X15 ) )
& ( true1 = X14 )
& ( ( true1 = X14 )
| ~ is_empty(vertex,t2tb(X8)) )
& ( is_empty(vertex,t2tb(X8))
| ( true1 != X14 ) ) )
& ! [X13: vertex1] : closure1(X12,X8,X11,X13)
& subset(vertex,t2tb(succ1(X9)),t2tb(X12))
& inv1(X0,X1,X12,X8,X11,X2) )
& ! [X10: vertex1] :
( closure1(X5,X8,X3,X10)
| ( X9 = X10 ) )
& shortest_path1(X0,X9,X2)
& inv1(X0,X1,X5,X8,X3,X2)
& ( X1 != X9 )
& ( tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 )
& mem(vertex,t2tb1(X9),t2tb(X4)) )
& ~ is_empty(vertex,t2tb(X4))
& ( true1 != X7 )
& ( ( true1 = X7 )
| ~ is_empty(vertex,t2tb(X4)) )
& ( is_empty(vertex,t2tb(X4))
| ( true1 != X7 ) ) )
& ~ $less(X2,0)
& ! [X6: vertex1] : closure1(X5,X4,X3,X6)
& ( is_empty(vertex,t2tb(X3))
| ~ is_empty(vertex,t2tb(X4)) )
& inv1(X0,X1,X5,X4,X3,X2) ),
inference(nnf_transformation,[],[f114]) ).
tff(f114,plain,
? [X0: vertex1,X1: vertex1,X2: $int,X3: set_vertex,X4: set_vertex,X5: set_vertex] :
( ? [X7: bool1] :
( ? [X8: set_vertex,X9: vertex1] :
( ? [X11: set_vertex,X12: set_vertex] :
( ? [X14: bool1] :
( ? [X15: set_vertex] :
( ? [X16: set_vertex] :
( ? [X17: $int] :
( ? [X18: vertex1] : ~ closure1(X12,X15,X16,X18)
& ( $sum(X2,1) = X17 ) )
& ( tb2t(empty(vertex)) = X16 ) )
& ( X11 = X15 ) )
& ( true1 = X14 )
& ( ( true1 = X14 )
<=> is_empty(vertex,t2tb(X8)) ) )
& ! [X13: vertex1] : closure1(X12,X8,X11,X13)
& subset(vertex,t2tb(succ1(X9)),t2tb(X12))
& inv1(X0,X1,X12,X8,X11,X2) )
& ! [X10: vertex1] :
( closure1(X5,X8,X3,X10)
| ( X9 = X10 ) )
& shortest_path1(X0,X9,X2)
& inv1(X0,X1,X5,X8,X3,X2)
& ( X1 != X9 )
& ( tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 )
& mem(vertex,t2tb1(X9),t2tb(X4)) )
& ~ is_empty(vertex,t2tb(X4))
& ( true1 != X7 )
& ( ( true1 = X7 )
<=> is_empty(vertex,t2tb(X4)) ) )
& ~ $less(X2,0)
& ! [X6: vertex1] : closure1(X5,X4,X3,X6)
& ( is_empty(vertex,t2tb(X3))
| ~ is_empty(vertex,t2tb(X4)) )
& inv1(X0,X1,X5,X4,X3,X2) ),
inference(flattening,[],[f113]) ).
tff(f113,plain,
? [X0: vertex1,X1: vertex1,X2: $int,X3: set_vertex,X4: set_vertex,X5: set_vertex] :
( ? [X7: bool1] :
( ? [X8: set_vertex,X9: vertex1] :
( ? [X11: set_vertex,X12: set_vertex] :
( ? [X14: bool1] :
( ? [X15: set_vertex] :
( ? [X16: set_vertex] :
( ? [X17: $int] :
( ? [X18: vertex1] : ~ closure1(X12,X15,X16,X18)
& ( $sum(X2,1) = X17 ) )
& ( tb2t(empty(vertex)) = X16 ) )
& ( X11 = X15 ) )
& ( true1 = X14 )
& ( ( true1 = X14 )
<=> is_empty(vertex,t2tb(X8)) ) )
& ! [X13: vertex1] : closure1(X12,X8,X11,X13)
& subset(vertex,t2tb(succ1(X9)),t2tb(X12))
& inv1(X0,X1,X12,X8,X11,X2) )
& ! [X10: vertex1] :
( closure1(X5,X8,X3,X10)
| ( X9 = X10 ) )
& shortest_path1(X0,X9,X2)
& inv1(X0,X1,X5,X8,X3,X2)
& ( X1 != X9 )
& ( tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 )
& mem(vertex,t2tb1(X9),t2tb(X4)) )
& ~ is_empty(vertex,t2tb(X4))
& ( true1 != X7 )
& ( ( true1 = X7 )
<=> is_empty(vertex,t2tb(X4)) ) )
& ~ $less(X2,0)
& ! [X6: vertex1] : closure1(X5,X4,X3,X6)
& ( is_empty(vertex,t2tb(X3))
| ~ is_empty(vertex,t2tb(X4)) )
& inv1(X0,X1,X5,X4,X3,X2) ),
inference(ennf_transformation,[],[f86]) ).
tff(f86,plain,
~ ! [X0: vertex1,X1: vertex1,X2: $int,X3: set_vertex,X4: set_vertex,X5: set_vertex] :
( ( ~ $less(X2,0)
& ! [X6: vertex1] : closure1(X5,X4,X3,X6)
& ( is_empty(vertex,t2tb(X4))
=> is_empty(vertex,t2tb(X3)) )
& inv1(X0,X1,X5,X4,X3,X2) )
=> ! [X7: bool1] :
( ( ( true1 = X7 )
<=> is_empty(vertex,t2tb(X4)) )
=> ( ( true1 != X7 )
=> ( ~ is_empty(vertex,t2tb(X4))
=> ! [X8: set_vertex,X9: vertex1] :
( ( ( tb2t(remove(vertex,t2tb1(X9),t2tb(X4))) = X8 )
& mem(vertex,t2tb1(X9),t2tb(X4)) )
=> ( ( X1 != X9 )
=> ( ( ! [X10: vertex1] :
( ( X9 != X10 )
=> closure1(X5,X8,X3,X10) )
& shortest_path1(X0,X9,X2)
& inv1(X0,X1,X5,X8,X3,X2) )
=> ! [X11: set_vertex,X12: set_vertex] :
( ( ! [X13: vertex1] : closure1(X12,X8,X11,X13)
& subset(vertex,t2tb(succ1(X9)),t2tb(X12))
& inv1(X0,X1,X12,X8,X11,X2) )
=> ! [X14: bool1] :
( ( ( true1 = X14 )
<=> is_empty(vertex,t2tb(X8)) )
=> ( ( true1 = X14 )
=> ! [X15: set_vertex] :
( ( X11 = X15 )
=> ! [X16: set_vertex] :
( ( tb2t(empty(vertex)) = X16 )
=> ! [X17: $int] :
( ( $sum(X2,1) = X17 )
=> ! [X18: vertex1] : closure1(X12,X15,X16,X18) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f67]) ).
tff(f67,plain,
~ ! [X10: vertex1,X21: vertex1,X25: $int,X24: set_vertex,X23: set_vertex,X22: set_vertex] :
( ( ~ $less(X25,0)
& ! [X1: vertex1] : closure1(X22,X23,X24,X1)
& ( is_empty(vertex,t2tb(X23))
=> is_empty(vertex,t2tb(X24)) )
& inv1(X10,X21,X22,X23,X24,X25) )
=> ! [X26: bool1] :
( ( ( true1 = X26 )
<=> is_empty(vertex,t2tb(X23)) )
=> ( ( true1 != X26 )
=> ( ~ is_empty(vertex,t2tb(X23))
=> ! [X27: set_vertex,X12: vertex1] :
( ( ( tb2t(remove(vertex,t2tb1(X12),t2tb(X23))) = X27 )
& mem(vertex,t2tb1(X12),t2tb(X23)) )
=> ( ( X12 != X21 )
=> ( ( ! [X1: vertex1] :
( ( X1 != X12 )
=> closure1(X22,X27,X24,X1) )
& shortest_path1(X10,X12,X25)
& inv1(X10,X21,X22,X27,X24,X25) )
=> ! [X28: set_vertex,X29: set_vertex] :
( ( ! [X1: vertex1] : closure1(X29,X27,X28,X1)
& subset(vertex,t2tb(succ1(X12)),t2tb(X29))
& inv1(X10,X21,X29,X27,X28,X25) )
=> ! [X30: bool1] :
( ( ( true1 = X30 )
<=> is_empty(vertex,t2tb(X27)) )
=> ( ( true1 = X30 )
=> ! [X31: set_vertex] :
( ( X28 = X31 )
=> ! [X32: set_vertex] :
( ( tb2t(empty(vertex)) = X32 )
=> ! [X33: $int] :
( ( $sum(X25,1) = X33 )
=> ! [X1: vertex1] : closure1(X29,X31,X32,X1) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(theory_normalization,[],[f60]) ).
tff(f60,negated_conjecture,
~ ! [X10: vertex1,X21: vertex1,X25: $int,X24: set_vertex,X23: set_vertex,X22: set_vertex] :
( ( $lesseq(0,X25)
& ! [X1: vertex1] : closure1(X22,X23,X24,X1)
& ( is_empty(vertex,t2tb(X23))
=> is_empty(vertex,t2tb(X24)) )
& inv1(X10,X21,X22,X23,X24,X25) )
=> ! [X26: bool1] :
( ( ( true1 = X26 )
<=> is_empty(vertex,t2tb(X23)) )
=> ( ( true1 != X26 )
=> ( ~ is_empty(vertex,t2tb(X23))
=> ! [X27: set_vertex,X12: vertex1] :
( ( ( tb2t(remove(vertex,t2tb1(X12),t2tb(X23))) = X27 )
& mem(vertex,t2tb1(X12),t2tb(X23)) )
=> ( ( X12 != X21 )
=> ( ( ! [X1: vertex1] :
( ( X1 != X12 )
=> closure1(X22,X27,X24,X1) )
& shortest_path1(X10,X12,X25)
& inv1(X10,X21,X22,X27,X24,X25) )
=> ! [X28: set_vertex,X29: set_vertex] :
( ( ! [X1: vertex1] : closure1(X29,X27,X28,X1)
& subset(vertex,t2tb(succ1(X12)),t2tb(X29))
& inv1(X10,X21,X29,X27,X28,X25) )
=> ! [X30: bool1] :
( ( ( true1 = X30 )
<=> is_empty(vertex,t2tb(X27)) )
=> ( ( true1 = X30 )
=> ! [X31: set_vertex] :
( ( X28 = X31 )
=> ! [X32: set_vertex] :
( ( tb2t(empty(vertex)) = X32 )
=> ! [X33: $int] :
( ( $sum(X25,1) = X33 )
=> ! [X1: vertex1] : closure1(X29,X31,X32,X1) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f59]) ).
tff(f59,conjecture,
! [X10: vertex1,X21: vertex1,X25: $int,X24: set_vertex,X23: set_vertex,X22: set_vertex] :
( ( $lesseq(0,X25)
& ! [X1: vertex1] : closure1(X22,X23,X24,X1)
& ( is_empty(vertex,t2tb(X23))
=> is_empty(vertex,t2tb(X24)) )
& inv1(X10,X21,X22,X23,X24,X25) )
=> ! [X26: bool1] :
( ( ( true1 = X26 )
<=> is_empty(vertex,t2tb(X23)) )
=> ( ( true1 != X26 )
=> ( ~ is_empty(vertex,t2tb(X23))
=> ! [X27: set_vertex,X12: vertex1] :
( ( ( tb2t(remove(vertex,t2tb1(X12),t2tb(X23))) = X27 )
& mem(vertex,t2tb1(X12),t2tb(X23)) )
=> ( ( X12 != X21 )
=> ( ( ! [X1: vertex1] :
( ( X1 != X12 )
=> closure1(X22,X27,X24,X1) )
& shortest_path1(X10,X12,X25)
& inv1(X10,X21,X22,X27,X24,X25) )
=> ! [X28: set_vertex,X29: set_vertex] :
( ( ! [X1: vertex1] : closure1(X29,X27,X28,X1)
& subset(vertex,t2tb(succ1(X12)),t2tb(X29))
& inv1(X10,X21,X29,X27,X28,X25) )
=> ! [X30: bool1] :
( ( ( true1 = X30 )
<=> is_empty(vertex,t2tb(X27)) )
=> ( ( true1 = X30 )
=> ! [X31: set_vertex] :
( ( X28 = X31 )
=> ! [X32: set_vertex] :
( ( tb2t(empty(vertex)) = X32 )
=> ! [X33: $int] :
( ( $sum(X25,1) = X33 )
=> ! [X1: vertex1] : closure1(X29,X31,X32,X1) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wP_parameter_bfs) ).
tff(f604,plain,
~ mem(vertex,t2tb1(sK22(sK12,sK17)),t2tb(succ1(sK17))),
inference(subsumption_resolution,[],[f600,f335]) ).
tff(f335,plain,
mem(vertex,t2tb1(sK17),t2tb(sK12)),
inference(resolution,[],[f214,f241]) ).
tff(f241,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex] :
( closure1(X0,X1,X2,X3)
| mem(vertex,t2tb1(X3),t2tb(X0)) ),
inference(cnf_transformation,[],[f175]) ).
tff(f600,plain,
( ~ mem(vertex,t2tb1(sK17),t2tb(sK12))
| ~ mem(vertex,t2tb1(sK22(sK12,sK17)),t2tb(succ1(sK17))) ),
inference(resolution,[],[f434,f336]) ).
tff(f336,plain,
~ mem(vertex,t2tb1(sK17),t2tb(sK14)),
inference(resolution,[],[f214,f242]) ).
tff(f242,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex] :
( closure1(X0,X1,X2,X3)
| ~ mem(vertex,t2tb1(X3),t2tb(X1)) ),
inference(cnf_transformation,[],[f175]) ).
tff(f434,plain,
! [X0: vertex1] :
( mem(vertex,t2tb1(X0),t2tb(sK14))
| ~ mem(vertex,t2tb1(X0),t2tb(sK12))
| ~ mem(vertex,t2tb1(sK22(sK12,sK17)),t2tb(succ1(X0))) ),
inference(resolution,[],[f341,f339]) ).
tff(f339,plain,
~ mem(vertex,t2tb1(sK22(sK12,sK17)),t2tb(sK12)),
inference(resolution,[],[f214,f245]) ).
tff(f245,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex] :
( closure1(X0,X1,X2,X3)
| ~ mem(vertex,t2tb1(sK22(X0,X3)),t2tb(X0)) ),
inference(cnf_transformation,[],[f175]) ).
tff(f341,plain,
! [X0: vertex1,X1: vertex1] :
( mem(vertex,t2tb1(X0),t2tb(sK12))
| mem(vertex,t2tb1(X1),t2tb(sK14))
| ~ mem(vertex,t2tb1(X1),t2tb(sK12))
| ~ mem(vertex,t2tb1(X0),t2tb(succ1(X1))) ),
inference(subsumption_resolution,[],[f340,f329]) ).
tff(f329,plain,
! [X0: uni] : ~ mem(vertex,X0,t2tb(sK9)),
inference(resolution,[],[f323,f223]) ).
tff(f223,plain,
! [X3: uni,X0: ty,X1: uni] :
( ~ is_empty(X0,X1)
| ~ mem(X0,X3,X1) ),
inference(cnf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: ty,X1: uni] :
( ( is_empty(X0,X1)
| ( mem(X0,sK19(X0,X1),X1)
& sort1(X0,sK19(X0,X1)) ) )
& ( ! [X3: uni] : ~ mem(X0,X3,X1)
| ~ is_empty(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f119,f159]) ).
tff(f159,plain,
! [X0: ty,X1: uni] :
( ? [X2: uni] :
( mem(X0,X2,X1)
& sort1(X0,X2) )
=> ( mem(X0,sK19(X0,X1),X1)
& sort1(X0,sK19(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f119,plain,
! [X0: ty,X1: uni] :
( ( is_empty(X0,X1)
| ? [X2: uni] :
( mem(X0,X2,X1)
& sort1(X0,X2) ) )
& ( ! [X3: uni] : ~ mem(X0,X3,X1)
| ~ is_empty(X0,X1) ) ),
inference(ennf_transformation,[],[f91]) ).
tff(f91,plain,
! [X0: ty,X1: uni] :
( ( ! [X2: uni] :
( sort1(X0,X2)
=> ~ mem(X0,X2,X1) )
=> is_empty(X0,X1) )
& ( is_empty(X0,X1)
=> ! [X3: uni] : ~ mem(X0,X3,X1) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: ty,X10: uni] :
( ( ! [X1: uni] :
( sort1(X0,X1)
=> ~ mem(X0,X1,X10) )
=> is_empty(X0,X10) )
& ( is_empty(X0,X10)
=> ! [X1: uni] : ~ mem(X0,X1,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_empty_def) ).
tff(f323,plain,
is_empty(vertex,t2tb(sK9)),
inference(subsumption_resolution,[],[f291,f319]) ).
tff(f319,plain,
! [X0: bool1] : sQ33_eqProxy(X0,X0),
inference(equality_proxy_axiom,[],[f289]) ).
tff(f289,plain,
! [X0: bool1,X1: bool1] :
( sQ33_eqProxy(X0,X1)
<=> ( X0 = X1 ) ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ33_eqProxy])]) ).
tff(f291,plain,
( is_empty(vertex,t2tb(sK9))
| ~ sQ33_eqProxy(sK13,sK13) ),
inference(equality_proxy_replacement,[],[f278,f289]) ).
tff(f278,plain,
( is_empty(vertex,t2tb(sK9))
| ( sK13 != sK13 ) ),
inference(definition_unfolding,[],[f208,f210]) ).
tff(f210,plain,
true1 = sK13,
inference(cnf_transformation,[],[f155]) ).
tff(f208,plain,
( is_empty(vertex,t2tb(sK9))
| ( true1 != sK13 ) ),
inference(cnf_transformation,[],[f155]) ).
tff(f340,plain,
! [X0: vertex1,X1: vertex1] :
( ~ mem(vertex,t2tb1(X0),t2tb(succ1(X1)))
| mem(vertex,t2tb1(X1),t2tb(sK14))
| mem(vertex,t2tb1(X1),t2tb(sK9))
| ~ mem(vertex,t2tb1(X1),t2tb(sK12))
| mem(vertex,t2tb1(X0),t2tb(sK12)) ),
inference(resolution,[],[f279,f240]) ).
tff(f240,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex,X5: vertex1] :
( ~ closure1(X0,X1,X2,X3)
| ~ mem(vertex,t2tb1(X5),t2tb(succ1(X3)))
| mem(vertex,t2tb1(X3),t2tb(X2))
| mem(vertex,t2tb1(X3),t2tb(X1))
| ~ mem(vertex,t2tb1(X3),t2tb(X0))
| mem(vertex,t2tb1(X5),t2tb(X0)) ),
inference(cnf_transformation,[],[f175]) ).
tff(f279,plain,
! [X16: vertex1] : closure1(sK12,sK9,sK14,X16),
inference(definition_unfolding,[],[f207,f211]) ).
tff(f211,plain,
sK11 = sK14,
inference(cnf_transformation,[],[f155]) ).
tff(f207,plain,
! [X16: vertex1] : closure1(sK12,sK9,sK11,X16),
inference(cnf_transformation,[],[f155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW672_2 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 20:06:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TF0_THM_EQU_ARI problem
% 0.14/0.36 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.74 % (13213)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2996ds/83Mi)
% 0.54/0.75 % (13207)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2996ds/34Mi)
% 0.54/0.75 % (13210)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2996ds/33Mi)
% 0.54/0.75 % (13208)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2996ds/51Mi)
% 0.54/0.75 % (13209)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.54/0.75 % (13211)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2996ds/34Mi)
% 0.54/0.75 % (13212)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.54/0.76 % (13214)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.58/0.77 % (13210)Instruction limit reached!
% 0.58/0.77 % (13210)------------------------------
% 0.58/0.77 % (13210)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77 % (13210)Termination reason: Unknown
% 0.58/0.77 % (13210)Termination phase: Saturation
% 0.58/0.77
% 0.58/0.77 % (13210)Memory used [KB]: 1525
% 0.58/0.77 % (13210)Time elapsed: 0.022 s
% 0.58/0.77 % (13210)Instructions burned: 34 (million)
% 0.58/0.77 % (13210)------------------------------
% 0.58/0.77 % (13210)------------------------------
% 0.58/0.77 % (13215)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on theBenchmark for (2996ds/55Mi)
% 0.58/0.77 % (13208)Instruction limit reached!
% 0.58/0.77 % (13208)------------------------------
% 0.58/0.77 % (13208)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77 % (13208)Termination reason: Unknown
% 0.58/0.77 % (13208)Termination phase: Saturation
% 0.58/0.77
% 0.58/0.77 % (13208)Memory used [KB]: 1370
% 0.58/0.77 % (13208)Time elapsed: 0.027 s
% 0.58/0.77 % (13208)Instructions burned: 52 (million)
% 0.58/0.77 % (13208)------------------------------
% 0.58/0.77 % (13208)------------------------------
% 0.58/0.77 % (13214)First to succeed.
% 0.58/0.77 % (13207)Instruction limit reached!
% 0.58/0.77 % (13207)------------------------------
% 0.58/0.77 % (13207)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77 % (13207)Termination reason: Unknown
% 0.58/0.77 % (13207)Termination phase: Saturation
% 0.58/0.77
% 0.58/0.77 % (13207)Memory used [KB]: 1489
% 0.58/0.77 % (13207)Time elapsed: 0.029 s
% 0.58/0.77 % (13207)Instructions burned: 34 (million)
% 0.58/0.77 % (13207)------------------------------
% 0.58/0.77 % (13207)------------------------------
% 0.58/0.77 % (13213)Also succeeded, but the first one will report.
% 0.58/0.77 % (13212)Instruction limit reached!
% 0.58/0.77 % (13212)------------------------------
% 0.58/0.77 % (13212)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77 % (13212)Termination reason: Unknown
% 0.58/0.77 % (13212)Termination phase: Saturation
% 0.58/0.77
% 0.58/0.77 % (13212)Memory used [KB]: 1592
% 0.58/0.77 % (13212)Time elapsed: 0.030 s
% 0.58/0.77 % (13212)Instructions burned: 45 (million)
% 0.58/0.77 % (13212)------------------------------
% 0.58/0.77 % (13212)------------------------------
% 0.58/0.77 % (13214)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13206"
% 0.58/0.78 % (13214)Refutation found. Thanks to Tanya!
% 0.58/0.78 % SZS status Theorem for theBenchmark
% 0.58/0.78 % SZS output start Proof for theBenchmark
% See solution above
% 0.58/0.78 % (13214)------------------------------
% 0.58/0.78 % (13214)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78 % (13214)Termination reason: Refutation
% 0.58/0.78
% 0.58/0.78 % (13214)Memory used [KB]: 1299
% 0.58/0.78 % (13214)Time elapsed: 0.017 s
% 0.58/0.78 % (13214)Instructions burned: 28 (million)
% 0.58/0.78 % (13206)Success in time 0.401 s
% 0.58/0.78 % Vampire---4.8 exiting
%------------------------------------------------------------------------------