TSTP Solution File: SWW672_2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW672_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.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 07:27:54 EDT 2024
% Result : Theorem 9.95s 1.79s
% Output : Refutation 9.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 100
% Syntax : Number of formulae : 143 ( 14 unt; 85 typ; 0 def)
% Number of atoms : 631 ( 214 equ)
% Maximal formula atoms : 60 ( 10 avg)
% Number of connectives : 773 ( 200 ~; 119 |; 352 &)
% ( 17 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 11 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 : 137 ( 54 >; 83 *; 0 +; 0 <<)
% Number of predicates : 25 ( 21 usr; 1 prp; 0-6 aty)
% Number of functors : 61 ( 58 usr; 27 con; 0-4 aty)
% Number of variables : 389 ( 205 !; 184 ?; 386 :)
% 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,
sK3: vertex1 ).
tff(func_def_34,type,
sK4: vertex1 ).
tff(func_def_35,type,
sK5: $int ).
tff(func_def_36,type,
sK6: set_vertex ).
tff(func_def_37,type,
sK7: set_vertex ).
tff(func_def_38,type,
sK8: set_vertex ).
tff(func_def_39,type,
sK9: bool1 ).
tff(func_def_40,type,
sK10: set_vertex ).
tff(func_def_41,type,
sK11: vertex1 ).
tff(func_def_42,type,
sK12: set_vertex ).
tff(func_def_43,type,
sK13: set_vertex ).
tff(func_def_44,type,
sK14: bool1 ).
tff(func_def_45,type,
sK15: set_vertex ).
tff(func_def_46,type,
sK16: set_vertex ).
tff(func_def_47,type,
sK17: $int ).
tff(func_def_48,type,
sK18: vertex1 ).
tff(func_def_49,type,
sK19: set_vertex > vertex1 ).
tff(func_def_50,type,
sK20: set_vertex > vertex1 ).
tff(func_def_51,type,
sK21: ( ty * uni ) > uni ).
tff(func_def_52,type,
sK22: ( ty * uni * uni ) > uni ).
tff(func_def_53,type,
sK23: ( ty * uni * uni ) > uni ).
tff(func_def_54,type,
sK24: ( vertex1 * vertex1 * $int ) > vertex1 ).
tff(func_def_55,type,
sK25: ( $int * vertex1 * vertex1 ) > vertex1 ).
tff(func_def_56,type,
sK26: ( $int * vertex1 * vertex1 ) > vertex1 ).
tff(func_def_57,type,
sK27: ( $int * vertex1 * vertex1 ) > vertex1 ).
tff(func_def_58,type,
sK28: ( $int * vertex1 * vertex1 ) > $int ).
tff(func_def_59,type,
sK29: ( vertex1 * vertex1 * $int ) > vertex1 ).
tff(func_def_60,type,
sK30: ( vertex1 * vertex1 * $int ) > $int ).
tff(func_def_61,type,
sK31: ( set_vertex * vertex1 ) > vertex1 ).
tff(func_def_62,type,
sK32: ( $int * vertex1 * vertex1 ) > $int ).
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 * vertex1 ) > $o ).
tff(pred_def_13,type,
sP1: ( $int * vertex1 * set_vertex ) > $o ).
tff(pred_def_14,type,
sP2: ( set_vertex * vertex1 * set_vertex * set_vertex * $int * vertex1 ) > $o ).
tff(pred_def_15,type,
sP33: ( vertex1 * vertex1 ) > $o ).
tff(pred_def_16,type,
sP34: ( vertex1 * vertex1 ) > $o ).
tff(pred_def_17,type,
sP35: ( vertex1 * vertex1 ) > $o ).
tff(pred_def_18,type,
sP36: ( vertex1 * set_vertex ) > $o ).
tff(pred_def_19,type,
sP37: ( vertex1 * $int * set_vertex * set_vertex ) > $o ).
tff(pred_def_20,type,
sP38: ( vertex1 * $int * vertex1 ) > $o ).
tff(pred_def_21,type,
sP39: ( $int * set_vertex * vertex1 ) > $o ).
tff(pred_def_22,type,
sP40: ( vertex1 * $int * set_vertex ) > $o ).
tff(pred_def_23,type,
sP41: ( $int * vertex1 * set_vertex ) > $o ).
tff(f53803,plain,
$false,
inference(subsumption_resolution,[],[f53773,f26755]) ).
tff(f26755,plain,
mem(vertex,t2tb1(sK31(sK13,sK18)),t2tb(succ1(sK18))),
inference(unit_resulting_resolution,[],[f267,f352]) ).
tff(f352,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex] :
( closure1(X0,X1,X2,X3)
| mem(vertex,t2tb1(sK31(X0,X3)),t2tb(succ1(X3))) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: set_vertex,X1: set_vertex,X2: set_vertex,X3: vertex1] :
( ( closure1(X0,X1,X2,X3)
| ( ~ mem(vertex,t2tb1(sK31(X0,X3)),t2tb(X0))
& mem(vertex,t2tb1(sK31(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,[sK31])],[f229,f230]) ).
tff(f230,plain,
! [X0: set_vertex,X3: vertex1] :
( ? [X4: vertex1] :
( ~ mem(vertex,t2tb1(X4),t2tb(X0))
& mem(vertex,t2tb1(X4),t2tb(succ1(X3))) )
=> ( ~ mem(vertex,t2tb1(sK31(X0,X3)),t2tb(X0))
& mem(vertex,t2tb1(sK31(X0,X3)),t2tb(succ1(X3))) ) ),
introduced(choice_axiom,[]) ).
tff(f229,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,[],[f228]) ).
tff(f228,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,[],[f227]) ).
tff(f227,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,[],[f175]) ).
tff(f175,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,[],[f174]) ).
tff(f174,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,[],[f128]) ).
tff(f128,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(f267,plain,
~ closure1(sK13,sK15,sK16,sK18),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
( ~ closure1(sK13,sK15,sK16,sK18)
& ( $sum(sK5,1) = sK17 )
& ( tb2t(empty(vertex)) = sK16 )
& ( sK12 = sK15 )
& ( true1 = sK14 )
& ( ( true1 = sK14 )
| ~ is_empty(vertex,t2tb(sK10)) )
& ( is_empty(vertex,t2tb(sK10))
| ( true1 != sK14 ) )
& ! [X16: vertex1] : closure1(sK13,sK10,sK12,X16)
& subset(vertex,t2tb(succ1(sK11)),t2tb(sK13))
& inv1(sK3,sK4,sK13,sK10,sK12,sK5)
& ! [X17: vertex1] :
( closure1(sK8,sK10,sK6,X17)
| ( sK11 = X17 ) )
& shortest_path1(sK3,sK11,sK5)
& inv1(sK3,sK4,sK8,sK10,sK6,sK5)
& ( sK4 != sK11 )
& ( sK10 = tb2t(remove(vertex,t2tb1(sK11),t2tb(sK7))) )
& mem(vertex,t2tb1(sK11),t2tb(sK7))
& ~ is_empty(vertex,t2tb(sK7))
& ( true1 != sK9 )
& ( ( true1 = sK9 )
| ~ is_empty(vertex,t2tb(sK7)) )
& ( is_empty(vertex,t2tb(sK7))
| ( true1 != sK9 ) )
& ~ $less(sK5,0)
& ! [X18: vertex1] : closure1(sK8,sK7,sK6,X18)
& ( is_empty(vertex,t2tb(sK6))
| ~ is_empty(vertex,t2tb(sK7)) )
& inv1(sK3,sK4,sK8,sK7,sK6,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18])],[f185,f194,f193,f192,f191,f190,f189,f188,f187,f186]) ).
tff(f186,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(sK5,1) = 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(sK3,sK4,X10,X7,X9,sK5) )
& ! [X17: vertex1] :
( closure1(sK8,X7,sK6,X17)
| ( X8 = X17 ) )
& shortest_path1(sK3,X8,sK5)
& inv1(sK3,sK4,sK8,X7,sK6,sK5)
& ( sK4 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(sK7))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(sK7)) )
& ~ is_empty(vertex,t2tb(sK7))
& ( true1 != X6 )
& ( ( true1 = X6 )
| ~ is_empty(vertex,t2tb(sK7)) )
& ( is_empty(vertex,t2tb(sK7))
| ( true1 != X6 ) ) )
& ~ $less(sK5,0)
& ! [X18: vertex1] : closure1(sK8,sK7,sK6,X18)
& ( is_empty(vertex,t2tb(sK6))
| ~ is_empty(vertex,t2tb(sK7)) )
& inv1(sK3,sK4,sK8,sK7,sK6,sK5) ) ),
introduced(choice_axiom,[]) ).
tff(f187,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(sK5,1) = 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(sK3,sK4,X10,X7,X9,sK5) )
& ! [X17: vertex1] :
( closure1(sK8,X7,sK6,X17)
| ( X8 = X17 ) )
& shortest_path1(sK3,X8,sK5)
& inv1(sK3,sK4,sK8,X7,sK6,sK5)
& ( sK4 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(sK7))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(sK7)) )
& ~ is_empty(vertex,t2tb(sK7))
& ( true1 != X6 )
& ( ( true1 = X6 )
| ~ is_empty(vertex,t2tb(sK7)) )
& ( is_empty(vertex,t2tb(sK7))
| ( 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(sK5,1) = 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(sK3,sK4,X10,X7,X9,sK5) )
& ! [X17: vertex1] :
( closure1(sK8,X7,sK6,X17)
| ( X8 = X17 ) )
& shortest_path1(sK3,X8,sK5)
& inv1(sK3,sK4,sK8,X7,sK6,sK5)
& ( sK4 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(sK7))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(sK7)) )
& ~ is_empty(vertex,t2tb(sK7))
& ( true1 != sK9 )
& ( ( true1 = sK9 )
| ~ is_empty(vertex,t2tb(sK7)) )
& ( is_empty(vertex,t2tb(sK7))
| ( true1 != sK9 ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f188,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(sK5,1) = 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(sK3,sK4,X10,X7,X9,sK5) )
& ! [X17: vertex1] :
( closure1(sK8,X7,sK6,X17)
| ( X8 = X17 ) )
& shortest_path1(sK3,X8,sK5)
& inv1(sK3,sK4,sK8,X7,sK6,sK5)
& ( sK4 != X8 )
& ( tb2t(remove(vertex,t2tb1(X8),t2tb(sK7))) = X7 )
& mem(vertex,t2tb1(X8),t2tb(sK7)) )
=> ( ? [X10: set_vertex,X9: set_vertex] :
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(X10,X12,X13,X15)
& ( $sum(sK5,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(sK10)) )
& ( is_empty(vertex,t2tb(sK10))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,sK10,X9,X16)
& subset(vertex,t2tb(succ1(sK11)),t2tb(X10))
& inv1(sK3,sK4,X10,sK10,X9,sK5) )
& ! [X17: vertex1] :
( closure1(sK8,sK10,sK6,X17)
| ( sK11 = X17 ) )
& shortest_path1(sK3,sK11,sK5)
& inv1(sK3,sK4,sK8,sK10,sK6,sK5)
& ( sK4 != sK11 )
& ( sK10 = tb2t(remove(vertex,t2tb1(sK11),t2tb(sK7))) )
& mem(vertex,t2tb1(sK11),t2tb(sK7)) ) ),
introduced(choice_axiom,[]) ).
tff(f189,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(sK5,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( X9 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(sK10)) )
& ( is_empty(vertex,t2tb(sK10))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(X10,sK10,X9,X16)
& subset(vertex,t2tb(succ1(sK11)),t2tb(X10))
& inv1(sK3,sK4,X10,sK10,X9,sK5) )
=> ( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK13,X12,X13,X15)
& ( $sum(sK5,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK12 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(sK10)) )
& ( is_empty(vertex,t2tb(sK10))
| ( true1 != X11 ) ) )
& ! [X16: vertex1] : closure1(sK13,sK10,sK12,X16)
& subset(vertex,t2tb(succ1(sK11)),t2tb(sK13))
& inv1(sK3,sK4,sK13,sK10,sK12,sK5) ) ),
introduced(choice_axiom,[]) ).
tff(f190,plain,
( ? [X11: bool1] :
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK13,X12,X13,X15)
& ( $sum(sK5,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK12 = X12 ) )
& ( true1 = X11 )
& ( ( true1 = X11 )
| ~ is_empty(vertex,t2tb(sK10)) )
& ( is_empty(vertex,t2tb(sK10))
| ( true1 != X11 ) ) )
=> ( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK13,X12,X13,X15)
& ( $sum(sK5,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK12 = X12 ) )
& ( true1 = sK14 )
& ( ( true1 = sK14 )
| ~ is_empty(vertex,t2tb(sK10)) )
& ( is_empty(vertex,t2tb(sK10))
| ( true1 != sK14 ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f191,plain,
( ? [X12: set_vertex] :
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK13,X12,X13,X15)
& ( $sum(sK5,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK12 = X12 ) )
=> ( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK13,sK15,X13,X15)
& ( $sum(sK5,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
& ( sK12 = sK15 ) ) ),
introduced(choice_axiom,[]) ).
tff(f192,plain,
( ? [X13: set_vertex] :
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK13,sK15,X13,X15)
& ( $sum(sK5,1) = X14 ) )
& ( tb2t(empty(vertex)) = X13 ) )
=> ( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK13,sK15,sK16,X15)
& ( $sum(sK5,1) = X14 ) )
& ( tb2t(empty(vertex)) = sK16 ) ) ),
introduced(choice_axiom,[]) ).
tff(f193,plain,
( ? [X14: $int] :
( ? [X15: vertex1] : ~ closure1(sK13,sK15,sK16,X15)
& ( $sum(sK5,1) = X14 ) )
=> ( ? [X15: vertex1] : ~ closure1(sK13,sK15,sK16,X15)
& ( $sum(sK5,1) = sK17 ) ) ),
introduced(choice_axiom,[]) ).
tff(f194,plain,
( ? [X15: vertex1] : ~ closure1(sK13,sK15,sK16,X15)
=> ~ closure1(sK13,sK15,sK16,sK18) ),
introduced(choice_axiom,[]) ).
tff(f185,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,[],[f184]) ).
tff(f184,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,[],[f183]) ).
tff(f183,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,[],[f135]) ).
tff(f135,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,[],[f134]) ).
tff(f134,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,[],[f61]) ).
tff(f61,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(f53773,plain,
~ mem(vertex,t2tb1(sK31(sK13,sK18)),t2tb(succ1(sK18))),
inference(unit_resulting_resolution,[],[f45273,f23848,f393]) ).
tff(f393,plain,
! [X3: vertex1,X0: set_vertex,X5: vertex1] :
( ~ mem(vertex,t2tb1(X5),t2tb(succ1(X3)))
| mem(vertex,t2tb1(X5),t2tb(X0))
| sP36(X3,X0) ),
inference(cnf_transformation,[],[f393_D]) ).
tff(f393_D,plain,
! [X0,X3] :
( ! [X5] :
( ~ mem(vertex,t2tb1(X5),t2tb(succ1(X3)))
| mem(vertex,t2tb1(X5),t2tb(X0)) )
<=> ~ sP36(X3,X0) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP36])]) ).
tff(f23848,plain,
~ mem(vertex,t2tb1(sK31(sK13,sK18)),t2tb(sK13)),
inference(unit_resulting_resolution,[],[f267,f353]) ).
tff(f353,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex] :
( ~ mem(vertex,t2tb1(sK31(X0,X3)),t2tb(X0))
| closure1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f231]) ).
tff(f45273,plain,
~ sP36(sK18,sK13),
inference(unit_resulting_resolution,[],[f376,f8143,f447,f8377,f394]) ).
tff(f394,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex] :
( ~ sP36(X3,X0)
| mem(vertex,t2tb1(X3),t2tb(X1))
| ~ mem(vertex,t2tb1(X3),t2tb(X0))
| ~ closure1(X0,X1,X2,X3)
| mem(vertex,t2tb1(X3),t2tb(X2)) ),
inference(general_splitting,[],[f348,f393_D]) ).
tff(f348,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex,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(cnf_transformation,[],[f231]) ).
tff(f8377,plain,
~ mem(vertex,t2tb1(sK18),t2tb(sK15)),
inference(unit_resulting_resolution,[],[f267,f350]) ).
tff(f350,plain,
! [X2: set_vertex,X3: vertex1,X0: set_vertex,X1: set_vertex] :
( ~ mem(vertex,t2tb1(X3),t2tb(X1))
| closure1(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f231]) ).
tff(f447,plain,
! [X0: uni] : ~ mem(vertex,X0,t2tb(sK10)),
inference(unit_resulting_resolution,[],[f407,f289]) ).
tff(f289,plain,
! [X3: uni,X0: ty,X1: uni] :
( ~ is_empty(X0,X1)
| ~ mem(X0,X3,X1) ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: ty,X1: uni] :
( ( is_empty(X0,X1)
| ( mem(X0,sK21(X0,X1),X1)
& sort1(X0,sK21(X0,X1)) ) )
& ( ! [X3: uni] : ~ mem(X0,X3,X1)
| ~ is_empty(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f140,f200]) ).
tff(f200,plain,
! [X0: ty,X1: uni] :
( ? [X2: uni] :
( mem(X0,X2,X1)
& sort1(X0,X2) )
=> ( mem(X0,sK21(X0,X1),X1)
& sort1(X0,sK21(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f140,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,[],[f99]) ).
tff(f99,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(f407,plain,
is_empty(vertex,t2tb(sK10)),
inference(trivial_inequality_removal,[],[f375]) ).
tff(f375,plain,
( is_empty(vertex,t2tb(sK10))
| ( sK14 != sK14 ) ),
inference(definition_unfolding,[],[f261,f263]) ).
tff(f263,plain,
true1 = sK14,
inference(cnf_transformation,[],[f195]) ).
tff(f261,plain,
( is_empty(vertex,t2tb(sK10))
| ( true1 != sK14 ) ),
inference(cnf_transformation,[],[f195]) ).
tff(f8143,plain,
mem(vertex,t2tb1(sK18),t2tb(sK13)),
inference(unit_resulting_resolution,[],[f267,f349]) ).
tff(f349,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,[],[f231]) ).
tff(f376,plain,
! [X16: vertex1] : closure1(sK13,sK10,sK15,X16),
inference(definition_unfolding,[],[f260,f264]) ).
tff(f264,plain,
sK12 = sK15,
inference(cnf_transformation,[],[f195]) ).
tff(f260,plain,
! [X16: vertex1] : closure1(sK13,sK10,sK12,X16),
inference(cnf_transformation,[],[f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWW672_2 : TPTP v8.2.0. Released v6.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 20:06:53 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % (20205)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (20208)WARNING: value z3 for option sas not known
% 0.14/0.39 % (20209)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (20211)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39 % (20208)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.40 % (20207)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 % (20212)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.40 % (20206)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (20210)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.40 % (20207)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.40 % (20207)Terminated due to inappropriate strategy.
% 0.14/0.40 % (20207)------------------------------
% 0.14/0.40 % (20207)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (20207)Termination reason: Inappropriate
% 0.14/0.40
% 0.14/0.40 % (20207)Memory used [KB]: 1012
% 0.14/0.40 % (20207)Time elapsed: 0.007 s
% 0.14/0.40 % (20207)Instructions burned: 12 (million)
% 0.14/0.40 % (20209)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.40 % (20209)Terminated due to inappropriate strategy.
% 0.14/0.40 % (20209)------------------------------
% 0.14/0.40 % (20209)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (20209)Termination reason: Inappropriate
% 0.14/0.40
% 0.14/0.40 % (20209)Memory used [KB]: 1014
% 0.14/0.40 % (20209)Time elapsed: 0.009 s
% 0.14/0.40 % (20209)Instructions burned: 13 (million)
% 0.14/0.40 % (20207)------------------------------
% 0.14/0.40 % (20207)------------------------------
% 0.14/0.40 % (20209)------------------------------
% 0.14/0.40 % (20209)------------------------------
% 0.14/0.40 % (20206)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.40 % (20206)Terminated due to inappropriate strategy.
% 0.14/0.40 % (20206)------------------------------
% 0.14/0.40 % (20206)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (20206)Termination reason: Inappropriate
% 0.14/0.40
% 0.14/0.40 % (20206)Memory used [KB]: 1012
% 0.14/0.40 % (20206)Time elapsed: 0.008 s
% 0.14/0.40 % (20206)Instructions burned: 12 (million)
% 0.14/0.40 % (20206)------------------------------
% 0.14/0.40 % (20206)------------------------------
% 0.22/0.42 % (20213)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.42 % (20214)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.42 % (20215)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.42 % (20213)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.42 % (20213)Terminated due to inappropriate strategy.
% 0.22/0.42 % (20213)------------------------------
% 0.22/0.42 % (20213)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.42 % (20213)Termination reason: Inappropriate
% 0.22/0.42
% 0.22/0.42 % (20213)Memory used [KB]: 953
% 0.22/0.42 % (20213)Time elapsed: 0.007 s
% 0.22/0.42 % (20213)Instructions burned: 11 (million)
% 0.22/0.42 % (20213)------------------------------
% 0.22/0.42 % (20213)------------------------------
% 0.22/0.44 % (20216)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 9.90/1.78 % (20214)First to succeed.
% 9.95/1.78 % (20214)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20205"
% 9.95/1.79 % (20214)Refutation found. Thanks to Tanya!
% 9.95/1.79 % SZS status Theorem for theBenchmark
% 9.95/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 9.95/1.79 % (20214)------------------------------
% 9.95/1.79 % (20214)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 9.95/1.79 % (20214)Termination reason: Refutation
% 9.95/1.79
% 9.95/1.79 % (20214)Memory used [KB]: 15927
% 9.95/1.79 % (20214)Time elapsed: 1.364 s
% 9.95/1.79 % (20214)Instructions burned: 2611 (million)
% 9.95/1.79 % (20205)Success in time 1.401 s
%------------------------------------------------------------------------------